Preheat oven to 350 degrees.
Roll out and press the crescent dough evenly into a 13" x 9" baking sheet, closing all the perforations.
Bake the dough in a preheated oven for 10-12 minutes.
Remove the dough from the oven and place the cheese slices evenly spaced over the top of the dough. Set aside.
While the dough is pre-baking heat the butter and oil a large skillet over medium/high heat.
Add the potatoes in an even layer in the skillet and allow to cook for 5 minutes without stirring.
Stir the potatoes and add 1 teaspoon salt, ½ teaspoon pepper, and the ham. Stir well.
Cook the potatoes and ham for an additional 5 minutes and remove from heat.
Carefully spoon the potatoes and ham mixture evenly over the partially baked crescent roll and cheese slices.
Use a spoon to make 8 wells in the hash brown potato mixture and carefully drop 8 eggs into the wells. Season the eggs with salt and pepper.
Place the hash brown breakfast pizza back into the oven to cook for an additional 20-25 minutes, or until the eggs are cooked to your desired preference.
Remove the pizza from the oven and top with the chopped scallions, if desired.
Cut the pizza into squares and serve hot.