In a large heavy-duty deep baking dish or Dutch oven, brown sausage over medium heat.
Add duck legs and cook until all legs are evenly browned, about 20 minutes.
Add onion and next 9 ingredients.
Stir to combine ingredients and add enough chicken broth to cover contents of dish.
Cover and place in a 400 degree oven for 1 1/2 hours.
Remove from oven and check for doneness.
Legs are done when the meat can be pulled off of the bone with minimal effort. Remove any legs that are done.
Add additional chicken broth as needed to just cover legs. Return covered dish to the oven for 30 minutes. Check for doneness every 30 minutes until all legs are tender.
Serve over warm rice.