Heat a large skillet over medium-high heat. Add hash browns, sausage, and bacon. Fry until lightly browned, 5 to 7 minutes. Transfer to a plate.
Preheat oven to 350 degrees F (175 degrees C).
Pour eggs into the hot skillet. Cook and stir until scrambled, 5 to 7 minutes. Transfer to the plate.
Line a 14-inch round pizza pan with 1 1/2 cans dough. Arrange remaining dough over a 9x13-inch baking pan; pinch the pieces together to prevent separation when baking.
Pour gravy mix into a small saucepan; whisk in 1 cup of cold water gradually. Cook over medium heat, stirring frequently, until gravy comes to a boil. Reduce heat and simmer for 1 minute. Allow to stand until thickened, about 4 minutes. Spread gravy over the dough; spread the hash brown mixture and cheese on top.
Bake in the preheated oven until crusts are golden, 35 to 45 minutes.