What Greek dish is scrambled eggs cooked with tomatoes and olive oil?

The Greek dish of scrambled eggs cooked with tomatoes and olive oil is strapatsada.

To make strapatsada, cooks simmer chopped or puréed tomatoes in olive oil until they thicken, then stir in beaten eggs and scramble them gently in the tomato sauce. Feta may be added near the end, while oregano, thyme, or pepper provide extra flavor. It can be served hot, cold, for breakfast, lunch, or as a light snack.

The dish is especially associated with regions where inexpensive, readily available ingredients made it practical home cooking. Summer tomatoes are particularly suitable because their sweetness and moisture create the sauce in which the eggs cook. The preparation is quick and does not require a separate omelette filling.

Strapatsada is also called kagianas in many Greek contexts, so that name is a defensible synonym rather than a different dish. It can resemble shakshouka, menemen, or huevos rancheros, but those dishes have different culinary traditions and usual preparation styles. Sfougato is a broader type of Greek omelette, not the canonical answer here.