The cuisine and table conduct would still be very similar to what you might have found in Imperial Rome during the time period historians still refer to as "Rome", with a few different ingredients of course and a distinctly Greek influence, it was leaner and Macedonian, Cretian and Romanian wine was favored.

Gamut, garos, and murri (think something resembling soy sauce\Worcestershire sauce, derived from fish and in virtually everything) seafood, poultry, a wide range of fruits and veggies for the upper-classes, honey, confections (like Turkish Delight), puls (like cream of wheat or oatmeal) flatbreads, olives, cheeses, and eggs. Butcher's meat was more expensive and eaten mainly by the upper classes, spices and seasonings were imported from all corners of the Empire to enhance Imperial dishes, and boiling was a primary method of cooking.

I answered someone on just what goodies the Romans were dining on here, that goes into much better detail

As for whether it would resemble Turkish cuisine, it does! Modern Greek, Turkish, and Balkan cuisine (including dishes resembling Baklava and tiropita, which are excellent btw, and descended from Roman placenta cake) is still very similar to the ingredients and recipes found in ancient\medieval times.