Whisk together eggs, milk, salt, and pepper. Set aside to allow the salt to break down the egg.
Spray an 8x8-inch baking dish with nonstick spray.
In a large skillet, cook sausage until almost all of the pink is gone. Add the onion and finish cooking the meat.
Using a slotted spoon, remove the meat and onions to a plate. Add hash browns to skillet and cook until lightly brown, flip and cook on the other side.
Place hash browns in bottom of lightly greased square pan. Top with sausage and 1/2 of each cheese.
Pour egg mixture over hash brown mixture and sprinkle with remaining cheese. Sprinkle a little fresh cracked pepper over the top.