Preheat your oven to 450°F (232°C).
In a skillet over medium heat, cook the crumbled breakfast sausage until browned and fully cooked, about 5-7 minutes. Drain any excess fat and set aside.
In a mixing bowl, whisk together the eggs, milk, salt, black pepper, and red pepper flakes (if using).
Heat the same skillet over medium-low heat. Pour in the egg mixture, stirring gently with a rubber spatula until just scrambled and slightly undercooked, about 3-4 minutes. Remove from heat.
Roll out the pizza crust onto the baking sheet or pizza stone if needed. If using a pre-made crust, you can simply place it on the baking surface.
Spread the cooked sausage evenly over the pizza crust.
Pour the scrambled eggs over the sausage layer, ensuring an even distribution.
Sprinkle the shredded cheddar cheese on top, followed by sliced green onions.
Bake in the preheated oven for 12-15 minutes, or until the cheese is bubbly and the crust is golden brown.
Remove from the oven, let cool for a few minutes, then slice into 8 pieces and serve.