Heat olive oil (or butter) in an 8-inch non-stick skillet over medium-low heat. Ensure the oil coats the bottom evenly.

Once the oil is shimmering, sprinkle the crumbled feta cheese evenly across the bottom of the hot skillet. Allow the feta to cook undisturbed for 2-3 minutes, until it starts to melt, brown, and form a crispy lace-like crust at the edges.

Carefully crack the two eggs directly over the crispy feta. You can place them side-by-side or slightly overlapping the feta crust.

Season the eggs with a pinch of salt, freshly ground black pepper, and optional red pepper flakes. Cover the skillet with a lid (or foil) and continue to cook for 3-5 minutes, or until the egg whites are fully set and the yolks are cooked to your desired consistency (runny, jammy, or firm).

Using a thin spatula, gently slide the crispy feta fried eggs from the skillet onto a plate. The feta should come up with the eggs, maintaining its crispy texture.

Garnish with fresh chopped parsley or dill, if desired. Serve immediately with a slice of toast or pita bread to soak up the runny yolks and flavorful feta oil.