Add a teaspoon of oil to a large skillet over medium heat. Add onions and cook until slightly softened.
Add sausage to the skillet and cook until no longer pink, breaking up into small pieces as it cooks. Drain off any excess grease.
Spray an 11x7 inch baking dish with nonstick cooking spray. Spread frozen hash browns in the bottom of the dish. Then sprinkle the sausage over the hash browns followed by the shredded cheese.
In a medium sized bowl, whisk eggs, milk and a pinch of salt and pepper together. Pour egg mixture evenly into the casserole dish.
Bake at 350 degrees, uncovered, for 40-45 minutes or until eggs are set. Let stand 5 minutes before serving. Serves 8.
Notes
For make ahead casserole - Prepare as directed in steps 1-4. Cover dish tightly with plastic wrap and refrigerate up to 24 hours. Bake at 350 degrees F for 45-50 minutes, uncovered. Let stand before serving.