In a large bowl, whisk together the eggs, milk, salt, and pepper until well combined.
Pour the egg mixture slowly and evenly over the sausage, vegetable, and cheese layers.
Sprinkle the remaining 1 cup of shredded cheese over the top.
Bake for 45 to 55 minutes, or until the eggs are set and the top is golden brown.
Let the casserole rest for 10 minutes before slicing and serving.
Notes
For a make-ahead option, assemble the casserole completely, cover it, and refrigerate for up to 24 hours. Add 10 to 15 minutes to the baking time if baking directly from the refrigerator.
You can substitute bacon or ham for the sausage.
If you prefer a crispier top, you can add the final layer of cheese during the last 10 minutes of baking.