Heat oven to 400°F: in a large baking dish (9×13) place the butter. Place the dish into the oven while it pre-bakes as that way it will grease the bottom of the dish. Once the oven is at 400, remove the greased casserole dish from the oven.
Spice the hash browns: Place the hash browns into the dish and cover the potatoes with all of the spices except the cayenne. Bake for 30 minutes. When they are done, lower the oven temperature to 375°F.
Get a large skillet out: While the potatoes are baking, you are going to cook the onion, pepper, and the sausage. In order to cook sausage properly be sure to check the instructions for whatever type of sausage you are using. Cook until the onions are soft and golden. The peppers should also be soft, and the sausage should be cooked through.
In a large bowl: When the food is done in the skillet, set it aside. In a large bowl, whisk the eggs, milk, and cayenne pepper. Set aside
Put it all together: When the hash browns are done, remove from the oven. Cover the potatoes with the sausage mixture. Be sure to really mix everything together, you want to get the flavors from the sausage mixture into those potatoes. Once it is all mixed together, cover the filling with cheese. Now, if you are looking to do a make-ahead breakfast casserole, you would pour the egg mixture on top of this, cover it with plastic wrap, and keep it in the fridge overnight (the next morning you would let it sit on the counter for 10-15 minutes while your oven heats up and then follow the rest of the instructions below). If you want to make it right away, cover it with the egg mixture, place in the oven for 40-45 minutes.
Check for doneness: at the 40-45 minute mark. The top should be cheesy and baked but you need to insert a toothpick or knife into the middle of the bake to make sure it is cooked. If it is a little bit jiggly when it comes out of the oven, that is okay, but you absolutely do not want liquid. If it is still liquid, place bake in the oven for 5 minute increments at a time. Once it is fully baked, let it sit on the counter for 5-10 minutes before cutting into it.