Preheat the oven to 400 degrees. Prepare two 17x11 inch baking sheets by lining them with parchment paper, setting them aside.
In a large bowl combine the eggs, milk, salt, and pepper. Pour the egg mixture onto the first 17x11 baking sheet. Place in the oven and bake for 15 to 17 minutes or until the eggs are set.
On the second baking sheet, place the sausage patties. Bake in the oven for 15 to 20 minutes or until cooked through but not overcooked. When done, transfer the sausage to drain on paper towels.
Place the sausage over the cooked eggs and cut the eggs into squares.
To assemble the sandwich, layer a bagel with the eggs, sausage, and cheese.