Place a small nonstick skillet over medium heat and lightly coat it with cooking oil or olive oil spray.
Crumble the feta directly into the skillet, arranging it in a rough circle with enough cheese around the outside to create crispy edges.
Cook the feta for about 1–2 minutes. Let it begin to melt and sizzle without allowing it to burn.
Carefully crack the egg into the center of the feta circle.
Sprinkle the egg with dried oregano and red pepper flakes.
Continue cooking over medium to medium-low heat until the egg white is completely set and the feta has developed a deep golden crust. Cook the yolk to your preferred doneness.
While the Crispy Feta Fried Eggs cook, warm the tortilla in a dry skillet, oven, or microwave. Alternatively, toast a slice of bread.
Mash the avocado over the warm tortilla or toast.
Squeeze a little fresh lemon juice over the avocado.
Once the feta is golden and crisp, carefully slide a thin spatula underneath the egg and cheese crust.
Transfer the crispy feta egg onto the avocado-topped tortilla.
Finish with pickled onions and a small drizzle of chili oil. Serve immediately while the feta edges are still crisp.