Preheat the Oven: Preheat the oven to 450°F (230°C).
Shape the Dough: Stretch or roll the pizza dough into a round measuring at least 12 inches across.
Prepare the Pizza Base: Place the shaped dough on a pizza stone or an oiled baking sheet.
Brush with Oil: Lightly brush the surface of the dough with the 1 tablespoon olive oil.
Add the Cheese and Vegetables: Evenly scatter the mozzarella, Parmesan, halved cherry tomatoes, sliced green onions, and half of the basil leaves over the oiled dough.
Add the Eggs: Carefully crack the 3 eggs directly over the arranged toppings and dough.
Season the Pizza: Sprinkle the sea salt and ground black pepper evenly over the eggs and toppings.
Bake the Pizza: Bake at 450°F (230°C) for 10 minutes, following the original cooking method, until the pizza is cooked and the toppings are heated through.