Heat the oven to 375°F. Squeeze the thawed hash browns in a clean towel until very dry, then toss with melted butter and 1/2 teaspoon salt.
Press the potatoes firmly across the bottom and 1 inch up the sides of a greased 9-by-13-inch dish. Bake for 18 minutes.
Meanwhile, brown the sausage in a skillet, breaking it into small crumbles, and drain it well. Scatter the sausage and cheddar over the hot potato base.
Whisk the eggs, milk, remaining salt, pepper and onion powder and pour into the dish.
Bake for 32 to 37 minutes more, until the center reaches 160°F. Rest 10 minutes before cutting.