Outside of monasteries, the intersection of men who were literate and men who were directly involved in food production was tiny.

Farming men weren’t cooking their midday meal out in the fields; they took some bread and maybe some protein out with them at the start of their working day.

> Outside of monasteries, the intersection of men who were literate and men who were directly involved in food production was tiny

Higher than that. While the educated men likely did not do much farm labor (depending on the local details they may have been out there during harvest when all hands were needed), they had to ensure there were enough slaves to do that. Most of them were also well aware that they were one bad harvest from starvation and so paid attention to food production.

> Farming men weren’t cooking their midday meal out in the fields; they took some bread and maybe some protein out with them at the start of their working day.

That depends on the culture. The famous Spanish dish Paella was men cooking in the fields.