Preheat the oven to 350º
Spray a deep 13x9 casserole dish with vegetable oil cooking spray.
Melt the butter in a large frying pan. Add the onion and saute over medium-low heat until soft, about 5 minutes. Add the hash browns and break apart. Saute until soft, about 5 minutes.
In a second frying pan, saute the sausage, breaking apart large clumps. When the sausage is cooked through, remove it from pan.
In a large mixing bowl, combine the milk, eggs, salt, pepper, nutmeg and mustard, briskly to blend.
To assemble, spread the onions and has browns evenly at the bottom of the greased dish. Place the bread cubes evenly on top of has browns. With a slotted spoon distribute sausage as the third layer. Pour the milk and egg mixture over over these layers. Add Parmesan as the next layer, while then adding the Cheddar.
Save a few tablespoons of Cheddar for the last 10 minutes of baking where you can add a fresh topping of melted cheddar.
Bake the casserole, uncovered for 45 to 50 minutes, until puffed and golden brown.