In a large pan or skillet over medium-high heat, melt butter and sauté onion and celery until softened. 6-8 minutes. Season generously with salt and pepper.
Add sausage and cook, breaking sausage up as you go, until browned and cooked through. Season with salt and pepper.
Transfer sausage mixture to a large bowl, then add in stuffing mix and dried cranberries. Pour in 1 1/4 cups chicken broth and stir until everything is combined and just moistened.
Preheat oven to 350º F.
To prepare apples: cut off the tops of each one, then take a tablespoon or melon baller and scoop out the core, making sure to leave at least 1/4-inch around the bottom and sides.
Spoon sausage stuffing mixture into cored apples, then transfer to a large baking dish. Pour remaining 1/4 cup chicken broth over the apples, then remaining 1/4 cup into the bottom of baking dish.
Place dish in oven and bake for 30-35 minutes, or until stuffing has browned and apples are tender.