Not silly at all! I'm not sure about cooking methods, but the crusades did introduce new foods to Europe, and the crusaders who lived in the Near East did sometimes adapt their eating habits to local customs.

To start off, when the crusaders arrived, Muslims noted that the food they ate was pretty gross (according to Muslim tastes, anyway). Christians and Muslims weren’t supposed to eat together. They considered each other’s food religiously unclean, and eating together might lead to other things, like maybe appreciating the other’s religion. Sharing food might also lead to sharing a bed...that was definitely forbidden. The Muslim poet and ambassador Usama ibn Munqidh talks about eating dinner with a Frankish knight in Antioch. That knight had acclimated to the east and no longer ate “Frankish food” which to Usama meant things like “garlic and mustard”, and especially pork. His Frankish friend had Egyptian chefs and only ate Muslim dishes. Maybe this knight wasn’t typical, but at least some of them adopted eastern customs.

The crusaders were also heavily involved in agricultural and trade. They especially learned to enjoy one product in particular:

"a most precious product, very necessary for the use and health of mankind, which is carried from here by merchants to the most remote countries of the world." (William of Tyre, vol. 2, pg 6)

This was sugar cane! This may be my favourite story from the entire history of the crusader states. They loved that sugar cane. They already knew about sugar beets, and they already used honey as a sweetener in Europe, but a big part of the crusader economy involved growing and exporting cane. They had big cane plantations outside of cities like Acre and Tyre, and cane processing factories inside the city.

According to Hans Mayer,

“The main exports to Europe were drugs and pharmaceutical goods including ginger, aloe, myrrh, camphor, senna leaves, bitter-wort, and the incense needed for liturgical purposes. There were spices like pepper, cinnamon, nutmeg, cloves, cardamom; fabrics and textiles like linen, silk, damask, muslin; dyes for use in European textile production, particularly alum (imported from Egypt), indigo, and brazilwood; fine wood (sandalwood); ivory, steel manufactures from Damascus, perfumes, pearls from the Orient, jewels, and porcelain. In addition there were the products of Outremer itself: castor sugar (produced mainly in Tyre and Acre), Jewish glassware, and Galilean wines. Exports to Egypt included salted fish, fruit (dates, oranges, and citrus fruit), olive oil, and oil of sesame. Grain, salt, pottery, and poultry were imported from Egypt for domestic consumption in Outremer.” (Mayer, pg. 175-176)

David Jacoby adds:

“Trade at the fonde was primarily related to the provisioning of Acre in basic victuals, such as grain, cheese, poultry, fruit and vegetables from Acre’s rural hinterland, marketed daily by Oriental Christian and Muslim peasants or by middlemen. They also brought raw materials and half-finished goods like flax, wool, silk, hides, straw for baskets and feathers for cushions and mattresses, in addition to wood used as fuel. Other products came from more distant regions, for example wine from the area of Nazareth in Lower Galilee, dates from around Tiberias and the Jordan Valley, and sugar from sugar cane plantations in widely scattered regions. The peasants also collected plants growing in coastal or arid and saline areas, from which soda ashes with high alkali content were produced. Soda ashes were one of two basic ingredients required for glassmaking and also entered in the production of soap and colourants for textiles. The peasants bought in Acre salt, ceramic containers and leather straps, among other goods.” (Jacoby, pg. 89)

And from Malcolm Barber:

“…farmers produced not only the Mediterranean staples of wheat, barley, olives and grapes with which they were already familiar, but crops new to them, including dates, sugar cane, figs, bananas and citrus fruit.” (Barber, pg. 227)

And one more from Adrian Boas:

“Fruit trees included apples, peaches, pistachios, plums, oranges, lemons, bananas (known as apples of paradise), figs, dates, pomegranates, almonds and carobs.” (Boas, pg. 79-80)

So, the crusaders jumped right into the agricultural and trade markets in the east, and they introduced lots of things to Europe that they had never seen before. They were especially amazed by sugar cane. They ate with Muslims sometimes and adopted Muslim eating habits, but they also introduced foods and products from Europe, just as much as they transported new products back to Europe.

Sources:

Primary sources:

William of Tyre, A History of Deeds Done Beyond The Sea, trans. E. A. Babcock and A. C. Krey (Columbia University Press, 1943, repr. Octagon Books, 1976).

Usama ibn Munqidh, The Book of Contemplation: Islam and the Crusades, trans. Paul M. Cobb (Penguin Classics, 2008)

Secondary sources:

Malcolm Barber, The Crusader States (Yale University Press, 2012)

Hans Mayer, The Crusades, 2nd ed., 1965, trans. John Gillingham (Oxford University Press, 1972)

David Jacoby, “Aspects of everyday life in Frankish Acre”, in Crusades, vol. 4 (2005)

Adrian J. Boas, Crusader Archaeology: The Material Culture of the Latin East (Routledge, 1999)