Melt butter in a large nonstick skillet over medium-high heat. Add sausage; cook 4 minutes or until browned. Transfer sausage to a large bowl, reserving drippings in skillet.
Add onion and next 7 ingredients to skillet; cook 8 minutes or until tender, stirring occasionally. Add vegetables and stuffing mix to sausage. Add broth, stirring just until moistened.
Spoon dressing into a greased 15" x 10" roasting pan.
Bake, covered, at 350° for 30 minutes. Uncover and bake 20 more minutes.