Preheat the oven to 375°F and spray an 8x8-inch baking pan with gluten-free nonstick cooking spray.
In a large bowl, whisk together the eggs and milk. Fold in the leftover stuffing. Spoon this mixture into the prepared baking dish. Cover evenly with shredded cheddar cheese.
Bake, uncovered, for 40-45 minutes, or until eggs are fully cooked.