Preheat the oven to 375 degrees. Coat the bottom of a rimmed baking sheet with 1-2 tablespoons of vegetable oil and set aside.
Peel the potatoes, discarding the skins, and grate them on the coarsest opening of a box grater. Place the grated potatoes in a large bowl and fill the bowl with cold water. Using your fingers, gently “wash” the potatoes for a few seconds, then transfer the potatoes to a colander to drain. Transfer back to the large bowl and repeat “washing” and draining. After draining for the second time, squeeze any extra water from the potatoes with your hands.
Mix the potatoes with the remaining 2 tablespoons of vegetable oil. Place on the prepared baking sheet, forming into a square or rectangle, pressing the potatoes to a thickness of about 1/3-1/2 inch. Bake for 30 minutes.
While the potatoes are baking, cook the bacon until crispy. Once cool enough to touch, cut into small pieces (about 1/4-1/2 inch squares). Cook the sausage if needed (I bought pre-cooked, frozen links, so I skipped this). Cut the sausage into bite-sized pieces.
When the potatoes have about 5 or 10 minutes left to bake, whisk together the eggs with salt and pepper. Scramble the eggs, removing from the stove when the eggs are still slightly wet in appearance.
Place the scrambled eggs on top of the hash brown crust. Scatter sausage and bacon on top of the eggs, then top with grated cheese. Return to the oven and bake for an additional 10 minutes.