Place sausage in a large, deep skillet. Cook over medium-high heat until evenly brown. Drain, and set aside.
Layer bread cubes, sausage, and Cheddar cheese in a lightly greased 7x11 inch baking dish. In a bowl, beat together the eggs, milk, salt, and mustard. Pour the egg mixture over the bread cube mixture. Cover, and refrigerate at least 8 hours or overnight.
Remove the casserole from the refrigerator 30 minutes before baking. Preheat oven to 350 degrees F (175 degrees C).
Bake 50 to 60 minutes in the preheated oven, or until a knife inserted in the center comes out clean. Let stand 10 minutes before serving.