Brush both sides of the flatbread with olive oil and toast in a 375°F oven or toaster oven for 3-4 minutes until lightly golden and crisp. This step is essential to prevent sogginess.
2 pieces flatbread, 2 tablespoons olive oil
Heat a non-stick or cast iron skillet over medium-low heat with 1 tablespoon olive oil. Crack eggs directly into the pan, season with salt and pepper, and cook for 3-4 minutes until whites are fully set but yolks remain runny. Cover skillet for the last minute to steam egg tops without flipping.
2 tablespoons olive oil, 4 large eggs, to taste salt, to taste black pepper
Sprinkle shredded mozzarella evenly over the warm toasted flatbread while it is still hot so the cheese begins melting from the residual heat. Use about ½ cup of cheese per flatbread.
1 cup mozzarella cheese, 2 pieces flatbread
Slide the cooked eggs onto the cheese-covered flatbread using a spatula, taking care to keep the yolks intact. If the cheese hasn't fully melted, place the assembled flatbread under the broiler for 1-2 minutes until bubbly.
4 large eggs, 1 cup mozzarella cheese, 2 pieces flatbread
Cut the flatbread into sections using a sharp knife or pizza cutter. Serve immediately while the base is crisp and the cheese is warm and bubbly. Avoid waiting more than 5 minutes to prevent sogginess.