Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease.
Beat 2 1/2 cups milk, eggs, and mustard in a large bowl.
Spread bread squares into the bottom of a baking dish. Layer mozzarella cheese atop the bread and top with sausage. Pour the egg mixture over the entire dish. Cover the baking dish with plastic wrap and refrigerate 8 hours to overnight.
Preheat oven to 300 degrees F (150 degrees C).
Stir cream of mushroom soup and 1 cup milk together in a bowl. Remove and discard plastic wrap from baking dish. Pour soup mixture over the ‘bake.’
Bake in preheated oven until hot in the center, about 90 minutes.