1. Bake muffin mix according to package directions in 2 (8-inch square) baking dishes. Cool and cut into 1-inch cubes. Preheat oven to 400°. Spread cornbread cubes in a single layer onto 2 (15- x 10- x 1-inch) jellyroll pans; bake 10 minutes or until lightly browned.
2. Cook sausage in a large skillet over medium-high heat, stirring often, 5 minutes or until browned. Remove from skillet with a slotted spoon. If less than 3 tablespoons of sausage drippings remains in skillet, add enough butter to make 3 tablespoons of liquid.
3. Add onion, celery, and carrot to skillet, and cook, stirring occasionally, 8 minutes or until softened. Stir in apple, and cook 5 minutes or until beginning to soften. Stir in broth, salt, and pepper. Transfer mixture to a large bowl; stir in sausage, cornbread cubes, eggs, and parsley. Transfer to a 9- x 13-inch greased baking dish. Bake, covered, at 350° for 25 minutes; uncover and bake 5 more minutes.
Prepare dressing up to a day in advance, and store, covered, in refrigerator. To reheat, bake, covered, in a preheated 350° oven for 25 minutes; uncover and bake 10 more minutes.