Lightly grease a 7x11-inch baking dish with butter or shortening; set aside.
(Optional) Heat a large, deep skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain.
Layer bread cubes, cooked sausage (if appropriate), and cheese in the prepared baking dish. Beat together milk, eggs, salt, and mustard in a medium bowl. Pour over bread mixture. Cover and refrigerate for 8 hours to overnight.
Preheat the oven to 350 degrees F (175 degrees C).
While the oven is heating, let casserole sit at room temperature for at least 30 minutes before baking.
Bake casserole in the preheated oven until a knife inserted into the center comes out clean, 50 to 60 minutes. Let casserole stand for 10 minutes before serving.
