Cook the tomatoes: Peel and finely dice the tomatoes. Melt the butter in a pan, when it's bubbling add the tomatoes (with all the juices and seeds) and cook for about 2-3 minutes until soft and thickened (they can't be runny).
Cook the eggs: Beat the eggs and season them with salt and pepper. Add the eggs to the pan, cook over low heat until almost cooked - they shouldn't be runny but also not cooked through.
Assemble the quesadillas: Sprinkle 1/4 of the cheese on one tortilla, top with 1/2 eggs, then sprinkle another 1/4 of the cheese and cover with a second quesadilla. Repeat with the other ingredients.
Brown the quesadillas: Heat 1 teaspoon of frying oil in a pan, when hot add one quesadilla into the pan. Cook over medium-high heat for a minute or so or until the quesadilla is golden brown (move the quesadilla once or twice to make sure it doesn't stick to the pan). Using a wide spatula, turn the quesadilla on the other side and cook until browned (you can also help yourself with a plate). Take off the pan and repeat with the other quesadilla.
Serve: Sprinkle quesadillas with salt. Divide them into 4 or 6 parts (pizza knife is great for that), serve with tomato salsa, sliced avocado, and cilantro.
Enjoy!