Preheat the oven to 350°F.
Heat the oil in a medium-sized skillet over medium-high heat. Once the oil is shimmery, add the sausage and cook until browned and cooked through, breaking it up as it cooks. Transfer the sausage to a paper towel–lined plate to drain and set aside.
Generously spray an 8x8-inch casserole dish with cooking spray. Layer 1 1/2 cups of the hash browns, half the sausage, and 3/4 cup of the cheese in the dish, then repeat with the remaining hash browns, sausage, and cheese.
In a large bowl, whisk together the eggs, milk, salt, and pepper. Pour over the ingredients in the dish. (Freezing instructions begin here.)
Bake, uncovered, for 50-60 minutes or until edges are bubbly, the middle is set, and top is golden. Tent with foil if the top starts to get too brown before it’s done. (Note: If the casserole was still cold when you put it in or if it was previously frozen, it will likely take longer. Our tests showed that it will take about 60 minutes to bake after being frozen and thawed. This is because of the extra liquid that's released during that process.)
Let the casserole sit for 10 minutes before serving. Serve warm, topped with hot sauce, salsa, or ketchup, if desired. Season with more salt and pepper, if desired.
Freeze For Later: Skip Step 1. Follow Steps 2-4, tightly wrap the casserole in plastic wrap or foil, and freeze.
Prepare From Frozen: Note: You may want to have hot sauce, salsa, or ketchup on hand for serving. Thaw completely. Follow Steps 5-6, except bake for about 60 minutes or until set in the middle.