I like the way the original receipt reads. "Take a porcyoun of Rys, & pyke hem clene, & sethe hem welle, & late hem kele; then take gode Mylke of Almaundys & do ther-to, & sethe & stere wyl; & do ther-to Sugre an honey, & serue forth." Helps if you know that "sethe" means "boil". The Italian version has units of measurement, and is very heavy on the sugar.
Way back in my college days in the vegetarian co-op, I started making something like this using leftover brown rice, soy milk, and brown sugar. All you do is put some brown rice in a saucepan, add enough non-dairy milk to cover, add sweetener to taste, bring to a boil and simmer. There's two thickening actions going on: boiling off of water from the liquid phase and expansion of the rice in the solid phase. The final pudding can be eaten warm or cold, and I think it's especially good for breakfast.
Hmm...methinks I need to make more examples of medieval cookery.