Grease a 9x13-inch baking dish and preheat oven to 350°F.
Brown sausage in a large skillet over medium, crumbling; drain excess fat and set aside.
Layer bread in dish; top with sausage and 1½ cups cheese.
Whisk eggs, milk, mustard, salt, pepper, and paprika in a large bowl.
Pour eggs evenly over bread and sausage; press gently with a spatula to help bread absorb liquid.
Cover and refrigerate overnight, or stand at least 30 minutes if baking immediately.
Bake covered with foil 30 minutes; uncover, top with remaining ½ cup cheese, and bake 15 minutes more until golden and set.
Rest 5 minutes; cut into squares and serve warm.