So I think one thing I need to stress is that the idea that the conflict and genocide of the 1930s and 1940s was at its heart a conflict over agricultural resources and a perceived food crisis is an argument that is specific to Timothy Snyder, and is a very controversial one. He develops the idea more in Black Earth, where he makes the argument that the Holocaust was essentially an act of "ecological panic", whereby Germany needed to secure food supplies against a biological Jewish enemy.

This is not a well-received argument in the history community. Historian Richard J. Evans (of Third Reich Trilogy fame) was pretty blunt in his review of the theory: "it really goes off the rails". Omer Bartov, writing about the arguments as presented in Bloodlands, was pretty blunt even in his title "How Not to Write a History of the Holocaust." Canadian historian Michael Marrus gave a more positive review of Black Earth, but still was lukewarm on the ecological/food security angle, finding that the book didn't really unlock any new understandings of the Holocaust. Further criticisms from historians on both of Snyder's books can be found in this New York Times article on the controversy.

So I would say food security = European warfare and genocide in the 20th century is at best considered an interesting idea by some historians, at worst considered flat-out an indefensible theory by many others. I should note in addition that I'm not aware of "mass hunger in Germany especially in the 1930s" except specifically with regards to poverty from the Great Depression - it's not like there were famines happening in Germany at the time.

I will point out that there was major US food relief to postwar Europe, directly through US programs like the Government and Relief in Occupied Areas (GARIOA) program, Food for Peace and the Marshall Plan, and also through the UN, such as United Nations Relief and Rehabilitation Administration (UNRRA) and the UN Food and Agricultural Organization (Organization (FAO). I'll also note that in the USSR, which was not part of these food aid programs, there was another famine in 1946-1947, which saw something like a million deaths (100,000 in Moldova, 300,000 in Ukraine, and 500,000 or so in Russia and Belarus). Much of Europe did also see major agricultural productivity rises after 1945, largely through mechanization, increased use of fertilizers and pesticides, and use of new hybrid seed varieties, as well as policies promoting their use, culminating in the Common Agricultural Program, initiated in 1962 by the European Economic Community. I am far from an expert on European agricultural policies, and would defer to any experts on that, but I'll note that War, Agriculture, and Food: Rural Europe from the 1930s to the 1950s, edited by Paul Brassley et al. seems like a good overview of the topic.

As for why there were no major wars in Europe after 1945, frankly a stronger argument is in the Cold War and the alliance systems it put into place (NATO and the Warsaw Pact). It meant that conflicts between alliance members in each alliance were kept to a minimum, and despite massive military mobilization and the ups and downs of the Cold War, both sides knew a conflict between the two alliances would result in World War III, and likely nuclear deployment. On top of this, the postwar borders and territorial integrity of European states was recognized by all European countries (bar Albania and Andorra) plus the US and Canada in the 1975 Helsinki Accords - this was interestingly an agenda item favored by the Eastern Bloc, as they had the most to gain through permanent recognition of the existing frontiers. I'll further note that this has largely held - even after 1991 all newly independent states in Europe have followed already-existing subnational borders and divisions, and no changes even to those borders have been widely internationally recognized, despite armed attempts to that end (whether in Cyprus, Bosnia, Croatia, Moldova or Ukraine).

So - the food security angle to European peace and war is a controversial one, and the postwar alliance system and international norms it put in place seems like a much more solid basis for understanding why territorial warfare in Europe after 1945 got rarer (but not nonexistent).

The hunger during the Great Recession in Germany was not caused by lack of agricultural products, but by the lack of money as a result of the economic crash and the ensuing mass unemployment. There were no structural problems with German agriculture.

The country with mass starvation in the 30's was the USSR. For this I will write a little bit more than for Germany. First of all, the 1932-33 famine (the Holodomor) was not the only one in USSR. There was another famine during the Civil war as a consequence of the disruptions of WW1, Civil war, mass requisitions from all sides and bad agricultural years. During the 20's, Lenin came up with a plan to allow farmers to sell their products (NEP) and the situation stabilized. Then, Stalin came and started forced industrialization and collectivization which disrupted the supply chains. Food production fell and a lot of the products were taken by the state in order to sell them abroad and use the hard currency to develop industry (heavy industry especially). On top of that, came another bad harvest year (1932) and the situation worsened. The party did not lowered the quotas needed to be taken by the state, and with the probable intention to hurt the Ukrainian regions even more, the entire policies resulted in mass starvation that is known as the Holodomor. Ukraine was not the only region where famine happened, the Volga region was affected too. While until 1941 large famines like Holodomor did not happened, all kinds of products (agricultural or not) were hard to find in the USSR because the idea of felling agricultural goods for cash in order to develop heavy industry was not abandoned.

Another important aspect regarding the soviet agriculture in the interwar period was its backwardness. While the land in Ukraine and other regions is one of the best in the world, the vast majority of farmers worked their lands with outdated practices and without machines. This was almost pre-modern like style of agriculture and the soviets tried to improve it. They tried to teach peasants in the collective farms new methods that were more productive, introduce better seeds and slowly but surely introduce machines (like tractors for example). They introduced the system of tractor stations that helped collective farms with modern machinery.

Now, obviously, WW2 disrupted the food security of Europe and famine, man made or not, appeared again. Here, for the western part of the continent (most notably Germany), the US stepped and brought food as help in the immediate post-war period. In the USSR things were not getting better as the loss of men and general disruption brought by the war, a bad harvest year in 1946 and not wanting the get help and thus appear weak, a new famine appeared in 1946-47 in USSR (it also happened to a lesser degree in Romania). This was to be the last famine in Europe.

Why no famine after this? Well, the general peace on the continent and the rebuilding efforts eliminated the disruptions of the war. Now for the two parts of Europe.

The West was not affected by famines before WW2 as there were no structural problems in agriculture and thus after the war, things began to enter their normal course. Soldiers came back to their farms (those who were farmers, obviously), the commercial routes began working again and grain and other products came to Europe from different places, one of the most important being USA. On the whole, this was not even a new phenomena as American food products (grain, corn, flour) came to Europe since the 1870's.

For the eastern part there were some changes in the new communist countries, but few changes in the USSR. Collectivization was implemented, but in some cases never finished as the opposition by the Church and peasants slowed the process and after Stalin's death was mostly abandoned. Poland and East Germany never collectivized their entire agriculture. The opposite was happening in Romania where the entire suitable land was collectivized by 1961. The USSR never introduced major changes after the war, but the process of mechanizing agriculture went ahead and thus increased the production. In a way, there was a pretty big difference in technology between 1930-50 in the east. On the other hand, since the early 60's and Khrushchev's failed agricultural reforms, the USSR started importing grains (from the US). Wars and large, forced changes in the agricultural systems were the main culprits of famine in USSR and those things did not happened after 1945.

There were no need to fight for land in the 50's Europe as food security was getting better because of peace und improving economy. Also, the only one who really wanted lebensraum was Hitler (and not because of lack of food) and he was gone.

UK managed to avoid the fear of starvation because it managed to import food from other places, also (and this is the case for other countries as well) the system of rationing was kept in place after WW2. UK ended rationing in 1954! 9 years after the war. Germany ended it in 1950 for most products. This is a good example to see that the food question did not improved immediately after 1945 as rationing was kept for years after that in some countries. In the USSR was even longer and products missing from the stores or being hard to find was more or less common.