Heat the oven. Arrange a rack in the middle of the oven and heat to 375°F. Coat a baking sheet with cooking spray.
Make the cheese sauce. Melt the butter in a small saucepan over medium-high heat. Add the flour and cook, stirring, until the butter-flour mixture loses its sheen, about 1 minute. Whisk in 1 cup of the milk and bring to a boil, whisking occasionally, until thickened, 3 to 4 minutes. Remove from the heat and whisk in 1/2 cup of the cheddar cheese and 1/4 teaspoon of the salt. Set aside to cool slightly while you make the rest of the toppings.
Cook the sausage and eggs. Heat a medium nonstick frying pan over medium-high heat. Crumble the sausage into the pan and cook until browned and cooked through, 5 to 7 minutes. While the sausage cooks, whisk together the eggs, remaining 1/4 cup of milk, and remaining 1/4 teaspoon salt in a medium bowl. Use a slotted spoon to transfer the cooked sausage to a paper towel-lined plate. Leave the sausage's fat in the pan and pour in the egg mixture. Scramble the eggs until almost cooked through but still moist, 3 to 4 minutes. Remove the pan from the heat.
Roll and dock the pizza dough. Roll or stretch the pizza dough out into a 12-inch round. Transfer the dough to the baking sheet. Use the tines of a fork to "dock" (poke holes in) the pizza dough, working from the middle out to within 1 inch of the edge. This will prevent the dough from getting soggy from the steaming cheese sauce.
Sauce the pizza. Spread on the cheese sauce in a thin, even layer as you would pizza sauce. You might not use all the cheese sauce.
Top the pizza. Sprinkle the sausage onto the cheese sauce, followed by the hash browns, and finally the scrambled eggs. Sprinkle the pizza with the mozzarella cheese, remaining 1/4 cup of cheddar cheese, and scallions.
Bake for 20 to 25 minutes. Bake until the cheese is melted and and the crust is golden-brown, 20 to 25 minutes.
Cool and slice. Let the pizza cool for 10 minutes; this gives the cheese sauce time to set and prevent it from oozing out. Transfer to a cutting board, slice, and serve.
In thinking about the pizza dough recipe I've made several times lately, in particular for the mini pizzas topped with caramelized balsamic onions and Parmesan, I decided a breakfastpizza would be just perfect for brunch
+ This BreakfastPizza Post brought to you by Jif® Peanut Butter +. We sat down and pow-wow’d and came up with some great breakfast ideas and some morning hack ideas that we think will help our family have fabulous mornings and maybe your family as well