1. Remove giblet packages from ducks, and reserve for another use. Rinse ducks, and pat dry; remove excess fat and skin. Place 1 duck and 1/2 cup balsamic vinaigrette each in 2 large zip-top plastic freezer bags; seal and chill 8 hours, turning occasionally.
2. Remove ducks from vinaigrette, discarding vinaigrette. Pat ducks dry, and prick legs and thighs with a fork, avoiding the breast area.
3. Melt butter in a large skillet over medium heat; add chopped green onions and celery, and sauté until tender. Remove from heat. Stir in cornbread stuffing, broth, chopped parsley, and pepper. Stuff each duck with half of mixture, and tie ends of legs together with string; tuck wing tips under. Place ducks, breast sides up, in a roasting pan.
4. Stir together molasses and hot sauce. Brush ducks evenly with about 3 Tbsp. molasses mixture.
5. Bake at 350° for 2 hours, brushing with remaining molasses mixture every 15 minutes during first 1 1/2 hours of baking or until leg joints move easily. Cover loosely with aluminum foil, and bake 30 more minutes or until an instant-read thermometer inserted in thickest portion of thigh registers 210° and internal temperature in center of stuffing registers 190°. Let stand 10 minutes. Garnish, if desired.
Sticky Chickens With Cornbread Dressing: Substitute 2 (4-lb.) whole chickens for ducks. Do not prick chickens. Proceed as directed. Bake at 350° for 1 hour and 45 minutes or until an instant-read thermometer inserted in thigh registers 180° and internal temperature in center of stuffing registers 190°.