Spray a 9x13-inch casserole with cooking spray.
Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Transfer to the prepared casserole.
Mix milk, Cheddar cheese, eggs, bread cubes, dry mustard, and salt together in a large bowl. Pour over the sausage. Cover and place in the refrigerator, 8 hours to overnight.
Preheat the oven to 350 degrees F (175 degrees C).
Bake casserole, uncovered, until a knife inserted in the center comes out clean, about 1 hour.