Remove casings from sausage. Cook sausage in a large nonstick skillet over medium-high heat until browned, stirring to crumble. Drain. Place sausage in a large bowl; add stuffing mix, tossing to combine.
Place stuffing mixture in a 13 x 9-inch baking dish coated with cooking spray. Drizzle stuffing mixture with broth and butter; sprinkle with cheese. Combine milk and remaining ingredients, stirring with a whisk; pour milk mixture over stuffing mixture.
Bake at 325° for 40 minutes or until set. Let casserole stand 5 minutes before serving.