Heat oil in a large sauté pan over medium-high heat. Add the finely diced onion and diced green bell pepper, sautéing them for about five minutes until softened while stirring occasionally.

Reduce the heat to medium, then add the canned diced tomatoes along with their juices, butter, Aleppo pepper, plus a generous pinch of salt and black pepper. Stir everything together until evenly combined and sauté for an additional two minutes until the tomatoes are heated through.

Crack the eggs directly on top of the tomato mixture in the pan. Allow them to cook undisturbed for about one minute before using a spoon to gently break the yolks; stir briefly into the tomato mixture while keeping some of the egg swirly on top.

Continue cooking until the eggs reach your desired level of doneness; traditionally, they should be just barely set yet still soft, which takes about three to four minutes total.

Once cooked, serve your Menemen hot from the pan with your choice of garnishes on top—like chives, parsley, crumbled feta cheese, or avocado slices—and pair it with some crusty sliced bread for dipping.