Kayanas se Psomi (Καγιανάς) is the Greek egg-and-tomato dish loaded into bread: scrambled eggs cooked down with tomato, often with cheese, eaten as a handheld instead of off a plate. The angle worth holding is that this is a tomato dish carrying eggs, not eggs with tomato as a garnish. Kayanas is built on tomato cooked until its water is gone and its sugar concentrates, and the eggs are folded into that base. Put into bread it becomes a warm, soft, savory sandwich, the kind eaten in the morning or as quick street food.
The build runs in a strict order and each step has a way to go wrong. Tomato goes into hot oil first and is cooked down hard until it darkens and the raw water has driven off, because a watery tomato base is the single most common failure and it soaks the bread to mush. Then the eggs go in and are stirred gently over lower heat so they stay soft and just set, folded through the tomato rather than scrambled dry. Cheese, when used, melts in at the end. The bread is a soft loaf or a warm flatbread, sometimes toasted lightly so it holds up under a wet filling. Done well, the tomato is jammy and concentrated, the eggs are soft and glossy, the cheese adds salt, and the bread takes some of the moisture without collapsing. Done poorly, it fails two predictable ways: a thin watery tomato that blows the bread out, or eggs cooked hard and rubbery so the whole thing turns dry and bland.
It shifts by what goes in beyond the base. Some cooks add onion or pepper into the tomato; others keep it strictly tomato and egg. The cheese choice swings it from mild to sharp. A version with cured pork or sausage cooked into the tomato is a richer preparation and deserves its own article rather than being crowded in here. What stays constant is the order: reduce the tomato until it is jammy and dry, fold soft eggs into it, and put it in bread that can take a little moisture without going to paste.