Heat a nonstick or cast iron skillet over medium heat.
Add olive oil and butter to the pan.
Scatter the crumbled feta evenly into the skillet and cook undisturbed for 2–3 minutes until the edges become golden and crispy.
Crack the eggs directly over the feta.
Cook until the egg whites are set but the yolks remain soft and runny.
In a small bowl, gently warm the chili oil with chili flakes and sesame seeds.
Transfer the eggs carefully onto a serving plate.
Spoon the warm chili oil over the eggs.
Finish with black pepper, fresh herbs, and optional toppings.
Serve immediately with toasted bread or warm pita.