In a large skillet, cook sausage over medium heat until brown. Drain off fat. If desired, remove crusts from bread. Cut bread into cubes.
Spread half of the sausage in the bottom of an ungreased 2-quart rectangular baking dish. Top with bread cubes; sprinkle with cheese. Top with the remaining sausage.
In a medium bowl, combine eggs, milk, salt, and dry mustard. Pour evenly over ingredients in dish. Press lightly with a rubber spatula or the back of a large spoon to moisten all of the bread. Cover and chill for 3 to 24 hours.
Preheat oven to 325 degrees F. Bake, covered, for 30 minutes. Bake, uncovered, for 15 to 20 minutes more or until a knife inserted near the center comes out clean. Let stand for 10 minutes before serving. Makes 8 servings.