Heat a large skillet over medium-high heat; cook and stir the sausage in the hot skillet until crumbly, evenly browned, and no longer pink.
Drain and discard any excess grease. Grease a 9x13 inch baking dish. Spread the bread cubes into the prepared dish; sprinkle the browned sausage and Cheddar cheese overtop.
Beat the eggs in a mixing bowl until smooth; add the salt, mustard powder, and 2 cups of milk and whisk until evenly blended. Pour the egg mixture over the bread cubes. Cover and refrigerate overnight.
Preheat an oven to 300 degrees F (150 degrees C). Whisk together the cream of mushroom soup and 1/2 cup milk; pour over the casserole.
Bake in the preheated oven until firm and golden brown, about 1 1/2 hours.