Preheat the oven to 350 degrees F. Lightly grease a 13- by 9-inch baking dish.
Cook the sausage in a large skillet over medium-high heat until thoroughly cooked, 8 to 10 minutes, stirring frequently; drain excess grease from the pan.
Beat the eggs, milk, and mustard in a large bowl with a wire whisk until well blended. Add the bread cubes; stir gently until evenly coated. Stir in the sausage and 1½ cups of the cheese.
Pour into the prepared baking dish; sprinkle the remaining cheese over the top of the casserole.
Bake until a knife inserted in the center comes out clean, 40 to 45 minutes.
Let stand 10 minutes before cutting into 12 squares to serve.