Any kind of sausage works in this versatile pie, so choose your favorite pre-cooked variety, or cook, grill or roast them up if they are raw. Don't be afraid to let the potato crust get really brown -- it will be deliciously crisp!
For the crust: Preheat the oven to 425 degrees F. Spray a 10-inch cast-iron skillet with nonstick spray.
Spread the hash browns over a layer of paper towels to air-dry for 10 to 15 minutes (alternatively, you can press them vigorously between layers of paper towels 2 to 3 times).
In a medium bowl, stir the dried hash browns, melted butter, Parmesan and pepper together. Press the mixture into the base and evenly up the sides of the prepared skillet. Transfer to the oven and bake until the potatoes begin to become golden brown and crisp, about 15 minutes.
Meanwhile, for the filling: Toss the sausage, scallions and 3/4 cup of the Cheddar in a medium bowl to combine.
In another medium bowl, whisk together the eggs, half-and-half, salt, pepper and hot sauce, if using.
Carefully press the sausage mixture into the browned crust. Pour the egg mixture over the sausage and sprinkle with the remaining 1/4 cup Cheddar. Carefully transfer the skillet to the oven. Bake until the crust is deeply browned and very crisp and the filling appears set when you gently shake the skillet, 35 to 40 minutes. Cool at least 10 minutes before slicing and serving. Serve warm or at room temperature.