Cook the sausage in a large skillet over medium heat, breaking it into small pieces as it browns.
Add the celery, onion, and shallots. Cook for 5–7 minutes, until softened.
Stir in the fresh herbs and black pepper.
Place the cornbread stuffing mix in a large bowl. Add the sausage mixture and gently toss to combine.
Melt the butter and combine it with the chicken broth. Gradually pour over the stuffing, stirring gently until evenly moistened. Add more broth if needed.
Transfer to a greased 3-quart smoker-safe baking dish.
Place the dish on the smoker uncovered and cook for 35–45 minutes, until heated through and lightly golden on top.