We do actually have a relatively good understanding of Byzantine cuisine. It would not be unreasonable to argue that atleast of the dishes and common food items were also available in the Balkans.

However the availability was probably dependent on the geographic location (ie. coast vs highland vs lowland), climate and or class, for example some exotic meats like donkey and peacock would only really be eaten regularly by the high nobility.

Generally, some common dishes would be various types of soup like lent soup. Stew, for which meat of all kind and fish was used. Even condiments like mustard and garum/γάρος (the infamous roman fish sauce) were used quite a bit. There would also be sausages like Loukanika, and grilled meat a kin to modern day souvlaki. Dried meats like, apokti/modern. apaki (made with pork loin), were quite popular. There was also a kind of hearty souflè like dish called Afrutum, which used minced chicken meat for its filling.

For dessert the general populace would have fruits, the nobility would enjoy them as well but they'd also have access to honey. A common treat among the nobles was a mixture made of honey and citron.

And of course bread would also be a staple food item, in the byzantine context there was also a version of bread with a high shelf life called Tragos/τραγός connected to the modern day Tarhanas.

You could probably find variations of these foods and dishes all over the Mediterranean and the balkans.

I'd recommend you the book "Tastes of Byzantium" by historian Andrew Dalby. He delves deeper into the topic, analysing the vraious sources going through the entire middle ages and explains its culinary history.