Remove the pizza dough from the refrigerator and let it come to room temperature.
Preheat the oven to 425°F (220°C) and line a rimmed baking sheet with parchment paper.
In a nonstick skillet, brown the ground breakfast sausage over medium heat, crumbling as it cooks; transfer to a paper towel-lined plate to drain.
Whisk the 6 eggs with 2 tablespoons milk and a pinch of salt and pepper.
Melt 2 tablespoons butter in the same nonstick skillet over medium heat, add the egg mixture and gently scramble until slightly undercooked; remove from heat and set aside.
On a lightly floured surface, roll the pizza dough into an approximately 10×16-inch rectangle.
Arrange the scrambled eggs and browned sausage down the center of the dough, leaving a border around the edges, then sprinkle 2 cups shredded cheese evenly over the filling.
Starting at the widest edge, roll the dough over the filling to form a log; pinch the seam and ends to seal and tuck the ends under the roll.
Place the stromboli seam-side down on the prepared baking sheet, brush the top with the egg wash (1 beaten egg mixed with 1 tablespoon water), then sprinkle with 1/4 teaspoon garlic salt and 2 tablespoons grated Parmesan.
Bake for 15 to 18 minutes, or until the crust is golden brown.
Let the stromboli cool for 5 minutes, then slice into portions and serve.