Preheat oven to 375ºF and butter a 9”x13” baking dish. Set aside.
Lay out squash and sweet potatoes on a rimmed baking sheet and toss with 1 tablespoon of fat. Bake in preheated oven, 20-25 minutes or until mostly cooked.
Meanwhile, in a large skillet over medium heat, sauté onion in remaining tablespoon of fat until translucent, 8-10 minutes. Add celery and continue to cook, 2-3 minutes. Add sausage and apple and cook, using a spoon to break up any large chunks, 6-8 minutes.
Using a large mixing bowl, combine squash, potatoes, sausage mixture, cranberries, pecans, fresh herbs and spices. Transfer mixture to prepared baking dish and add broth or cider to the top.
Cover tightly with aluminum foil and bake in preheated oven, 15-20 minutes. Serve warm.