In a skillet over medium heat, melt the butter. Add the ground breakfast sausage and cook until browned, breaking it apart with a spatula. Drain excess fat and transfer to a bowl.
In the same skillet, whisk together the eggs, milk, salt, and pepper. Pour into the skillet and scramble until just set. Remove from heat and combine with the sausage. Stir in the cheese.
Preheat your oven to 375°F (190°C). Roll out the pizza dough into a rectangle, about 12x16 inches in size.
Spread the sausage and egg mixture evenly over the dough, leaving about an inch around the edges. Sprinkle garlic salt and Parmesan cheese over the filling.
Starting from one of the long edges, roll the dough tightly over the filling. Pinch seams to seal. Place seam-side down on a parchment-lined baking sheet.
Brush the top of the stromboli with the egg wash and cut slits on top to allow steam to escape. Bake for 25-30 minutes or until golden brown.
Let cool for a few minutes before slicing. Serve warm and enjoy!