Turkish Fried Eggs with Pickled Onion

In a small bowl, toss onion with lime juice and a pinch of salt; let marinate. Spread yogurt on two plates. Set aside. Add butter and chile flakes to a large skillet over medium heat and melt until foamy. Crack eggs into skillet and fry until whites are set and yolks are runny, about 3 minutes. Slide eggs onto plate over yogurt and pour remaining chile butter over top. Top eggs with onion and mint leaves. Serve with toasted pita.