Long story short, this question was inspired by my looking at Google Earth. I looked around modern day Iran trying to find green: something that appears like it could support enough agriculture to support 100,000 strong armies. I failed. Iran appears to be very mountainous, lacking in any major rivers that I could find, and the land in general seems to be nothing but scrub-brush covered dirt. Even now in 2017 satellite images I can't find any vast agricultural areas that you might find in, say, the American midwest.
How did they do it?
I'm not sure I understand the premise of your question. The present population of Iran, which is not (and has never been) under particular threat of famine is 80 million people. Nor was it under such threat before the discovery of oil.
There are credible reasons to believe that Persia underwent permanent desertification during the Mongol conquests, but in terms of the overall size of the population and amount of available land, I don't see any reason to be skeptical that even under present environmental conditions the country of Iran would have been able to field enormous armies.
We can also see an example of this from pure deserts. In their conquests in the 7th century, the Arabs were able to field armies that numbered into the tens of thousands despite emerging from far harsher conditions.