Remove casings from sausage. Cook sausage in a large nonstick skillet over medium heat until browned; stir to crumble. Remove from pan. Add onion and mushrooms to pan; cook 5 minutes or until onion is tender and moisture evaporates. Remove from heat. Add sausage; stir to combine.
Combine milk and next 5 ingredients (through eggs) in a medium bowl, stirring with a whisk.
Arrange half of bread in a 13 x 9-inch baking dish coated with cooking spray. Spoon half of sausage mixture evenly over bread; sprinkle with 1/4 cup cheese. Top with remaining bread. Spoon remaining sausage mixture over bread; sprinkle with remaining 1/4 cup cheese. Pour egg mixture evenly over bread mixture. Cover and chill overnight.
Preheat oven to 350°.
Bake, uncovered, at 350° for 35 minutes or until browned. Let stand 10 minutes before serving.