1. Place oven rack on lowest shelf. If you have a stone, place it on rack. Preheat oven to 550°F, or your oven’s highest temperature, for 45 minutes.
2. Cook bacon in a skillet over medium heat, stirring occasionally, until still soft but beginning to crisp at edges, 5 minutes. Transfer to a paper towel-lined plate to drain.
3. Generously dust a 14-inch-wide pizza peel with cornmeal. Flatten a dough ball on top. Using lightly floured fingers or a floured rolling pin, stretch dough into a 6- to 7-inch round. (Make sure crust slides around easily on peel. Add more cornmeal under pizza if necessary. ) Brush 1 tsp. oil over crust.
4. Sprinkle 1 Tbsp. mozzarella, then a quarter of bacon, another 1 Tbsp. mozzarella and 1½ tsp. Parmesan over crust. Gently crack an egg over center of pizza.
5. Carefully slide pizza onto stone, using a spatula to ease pizza onto stone without spilling egg. Bake until crust is slightly charred on top and golden on bottom (lift an edge to check), cheese has melted and egg white is cooked but yolk is still jiggly, about 6 1/2 minutes. While pizza is cooking, make 3 more using remaining ingredients. Bake remaining pizzas. Using peel, transfer pizzas to individual plates. Sprinkle with scallions and pepper, then serve immediately.