After a word in the genitive, we cannot have a definite noun in Swedish. You don't do that in English either: you don't say the cooks' the food.
The fact that we know the food is owned by someone is enough to make the other noun definite by extension (or, since we already know the food is not just any food, but the cooks' food, it is definite semantically). So if you would re-phrase the cooks' food into an 'of' construction, both the cooks and the food need to be definite.
Therefore, kockarnas mat is equivalent to the food of the cooks, not food of the cooks.