Heat olive oil in a non-stick skillet over medium heat until shimmering. Place feta slices in the pan with space between each piece.
Cook the feta undisturbed for 2 to 3 minutes until bottoms turn golden brown and crispy. The cheese will soften slightly but shouldn't completely melt.
Carefully crack one egg next to each feta piece, keeping yolks intact. Sprinkle oregano and red pepper flakes over everything.
Reduce heat to medium-low and cover the pan with a lid. Cook for 3 to 4 minutes until egg whites are completely set but yolks remain runny.
Use a thin spatula to gently lift each egg with its feta piece onto serving plates. Garnish with fresh parsley and dill. Serve immediately while crispy.