Preheat oven to 500 degrees F (260 degrees C). Grease a sheet pan with 1 tablespoon oil.
Cook and crumble bacon.
Combine mozzarella and Parmesan in a bowl; set aside.
Combine Shamrock Farms Cottage Cheese, oregano, black pepper, and cayenne pepper, and 1 tablespoon oil in a bowl; set aside.
Press and roll dough into a 15x11-inch rectangle on a floured counter. Transfer to the sheet pan and press dough to the edges. Brush edges with remaining 1 tablespoon oil.
Parbake dough for 5 minutes; remove from oven.
Spread cottage mixture evenly over the crust, leaving a 1-inch border around the edges. Sprinkle bacon over cottage cheese mixture. Sprinkle mozzarella mixture over the top. Make 2 rows of 3 small wells in the cheese, each about 3 inches across. Crack 1 egg into each well. Season with salt and pepper.
Return to the oven and bake 9 to 10 minutes for slightly runny yolks, longer if you want them firmer. Cool slightly and sprinkle with scallions and chives.