01 - Preheat oven to 425°F. Line a baking sheet with parchment paper or lightly oil a pizza stone.
02 - Roll out the pizza dough into a 12-inch circle and transfer to the prepared sheet. Brush evenly with olive oil.
03 - Bake the crust for 5 minutes to set. Remove from oven and set aside.
04 - In a mixing bowl, whisk eggs, milk, salt, and black pepper until blended.
05 - Melt butter in a nonstick skillet over medium heat. Pour in the egg mixture and scramble gently until just set but still soft. Remove from heat.
06 - Evenly spread the scrambled eggs over the parbaked crust.
07 - Distribute mozzarella and cheddar cheeses evenly over the eggs.
08 - Scatter sausage or bacon (if using), diced bell pepper, and sliced red onion over the cheese.
09 - Return pizza to oven and bake for 8 to 10 minutes, or until cheese is melted and bubbly and crust is golden brown.
10 - Remove from oven. Top with chives or green onions, slice, and serve immediately while hot.