I wonder if this means that we make chicken with rice for every meal, or if every time we make chicken we also make rice. (I don't always make chicken, but when I do, I make chicken with rice. I am the most boring chef in the world.)
the translation should be cook.
because make it's more like "we build chicken with rice"
"Make" is used often like this to mean "cook" or "to prepare" food.
Also in French, we use faire=make, I make a cake=je fais un gâteau.
Cocinar and hacer are different, just like cook and make are.