6 slices bacon
8 ounces (2 cups) mozzarella cheese, shredded
1 ounce (½ cup) Parmesan cheese, grated
4 ounces (½ cup) small-curd cottage
¼ teaspoon dried oregano
Salt and pepper
Pinch cayenne pepper
1 pound store-bought pizza dough, room temperature
1 tablespoon extra-virgin olive oil
6 large eggs
2 scallions, sliced thin
Adjust oven racks to middle and lowest positions and heat oven to 400 degrees. Place bacon in single layer on rimmed baking sheet and cook on upper rack until crisp, about 15 minutes, rotating sheet halfway through baking. Transfer bacon to paper towel–lined plate, let cool slightly, then crumble. Transfer rendered bacon fat to small bowl and reserve. Let sheet cool to room temperature, about 10 minutes.
Increase oven temperature to 500 degrees. Combine mozzarella and Parmesan in bowl. In separate bowl, combine cottage cheese, oregano, ¼ teaspoon pepper, cayenne and 1 tablespoon reserved bacon fat. Brush 1 tablespoon bacon fat over cooled, now-empty sheet.
Press and roll dough into 15 by 11-inch rectangle on lightly floured counter, then transfer to prepared sheet and push to edges of pan. Brush edges of dough with oil. Bake on lower rack until top of crust appears dry and bottom is just beginning to brown, about 5 minutes.
Remove sheet from oven and press on air bubbles with spatula to flatten. Spread cottage cheese mixture evenly over crust, leaving 1-inch border around edge, then sprinkle with crumbled bacon and cheese mixture. Using back of spoon, hollow out six 3‑inch-wide holes in cheese. Crack 1 egg into each hole and season each with salt and pepper.
Continue to bake pizza until crust is light golden around edges and eggs are just set, 9 to 10 minutes for slightly runny yolks or 11 to 12 minutes for soft-cooked yolks, rotating sheet halfway through baking.
Remove sheet from oven. Transfer pizza to cutting board and let cool for 5 minutes. Sprinkle with scallions, slice, and serve.