Preheat oven to 375°F (190°C). Grease a 9×13-inch baking dish.
Cook sausage in a skillet over medium heat until browned and crumbled. Drain excess fat.
Spread cooked sausage evenly in the prepared baking dish.
Sprinkle shredded cheese over the sausage.
In a bowl, whisk eggs, milk, salt, pepper, and paprika until smooth.
Pour egg mixture evenly over the sausage and cheese.
Bake uncovered for 35–40 minutes, until the center is set and the top is lightly golden.
Let rest for 5 minutes before slicing and serving.