Heat oven to 350 degrees. Remove hash browns from refrigerator and let rest. In skillet, cook sausage according to package directions.
Lightly grease two 12-cup muffin tins. In bowl, whisk eggs and milk. Add hash browns, butter, ham, red pepper, black pepper, and cheese; mix.
Fill muffin tins 2/3 full; bake 27-30 minutes. Serve warm.