Heat the olive oil in a large skillet or sauté pan over medium-high heat.
Add the diced onion and green pepper. Cook for about 5 minutes, stirring occasionally, until the vegetables have softened.
Reduce the heat to medium. Add the diced tomatoes with their juices, butter, Aleppo pepper, salt, and freshly cracked black pepper.
Stir everything together and cook for another 2–3 minutes, allowing the tomatoes to become hot and slightly saucy.
Crack the eggs directly over the tomato mixture. Leave them undisturbed for about 1 minute.
Gently break the yolks with a spoon or spatula and partially stir the eggs through the tomatoes and peppers. Avoid vigorously scrambling them; leaving visible swirls of egg gives this Menemen Recipe its characteristic soft texture.
Continue cooking for approximately 2–3 minutes, or until the eggs are just set but still soft and creamy. Cook a little longer if you prefer firmer eggs.
Remove the skillet from the heat and add your preferred garnishes. Serve immediately with warm crusty bread.