Contemporary Americans don't eat the same dishes as Medieval Europeans because because many foods in a modern American diet were not available to Medieval Europeans. They either hadn't been discovered by Europeans yet, such as New World foods like maize, potatoes, and chocolate, or were unavailable for other reasons, such as pepper and other spices, which were expensive luxuries then.

When devising recipes, medieval cooks like Taillevent had to take into account the amount of leftovers and how perishable they would be given the lack of refrigeration as well as how reliable his supply of quality ingredients was. Almond milk, for example, used to be commonplace for a number of reasons. In addition to its inherent perishability, cow's milk was often sold by unscrupulous dealers who adulterated their product or sold spoiled milk as fresh. Almonds were much less perishable and a reliable supply could be kept on hand.

Old recipes are often the best that a cook could devise given the constraints at the time. Mooncakes, for example, have decreased in popularity as the Chinese community has been exposed to lighter goodies like Portugese egg tarts and Australian (no, I don't mean Austrian) apple strudel and adopted them as their own.

Now if you'll excuse me, I'm hungry.