Island Style - Ionian is the western reading of the Greek filled bread, and the one with an Italian accent running through it. The angle worth holding is that long Venetian contact left a real mark on Ionian cooking: more olive oil and fewer hard cures, tomato treated as a sauce rather than a raw slice, and a comfort with cheese and braised meat that reads closer to the Italian side of the sea. An Ionian filled bread is softer, richer, and more sauced than the spare island wraps of the Aegean.
The build starts from a soft wheat bread or a roll with enough crumb to hold a wet filling, because the Ionian style runs to braises and sauces rather than dry cures. The protein is often slow-cooked meat in a tomato or wine reduction, or a cheese-forward filling, spooned in while warm so the bread takes some of the sauce. Olive oil is generous, herbs lean toward the Italian register, and a sharp grated cheese frequently finishes it. Done well, the bread absorbs enough sauce to flavor without disintegrating, the braise is reduced tight rather than soupy, and the cheese gives a salt edge against the sweet tomato. Done poorly, it goes wrong two ways: a braise left too loose so the bread blows out before the second bite, or so much oil and cheese that the dish turns heavy with nothing acidic to lift it.
The variation across the Ionian islands is by which Venetian habit each kept. A wine-braised-meat reading on one island, a tomato-and-cheese one on another, an oil-and-herb version where the groves are old: each is its own local preparation and deserves its own article rather than being crowded in here. What stays constant is the Italian influence working through Greek hands. Reduce the sauce until it clings instead of runs, build on bread with enough crumb to soak a little and hold, and let a sharp cheese do the cutting that capers and cured fish do further east. The Ionian filled bread tastes of two cuisines that lived next to each other long enough to blend.