"We are eating Italian food."
Translation:İtalyan yemeği yiyoruz.
I think that the -i here is not accusative but possessive, joining the "İtalyan" and "yemek" together.
Basically, Turks don't say "English food, Turkish food" but "Englishman food, Turk food" (i.e. with the noun representing the nationality), and so it needs a possessive on the second noun in this half-genitive construct.