If using homemade cornbread, you will need an 11-inch by 8-inch pan of cornbread. Serves 8 to 10
1. Adjust oven racks to upper-middle and lower-middle positions and heat oven to 250 degrees F. Bake cornbread on 2 baking sheets until dried and crisp, 50 to 60 minutes. Cool completely, then transfer to large bowl.
2. Increase oven temperature to 400 degrees. Mix cherries and 1/2 cup broth in small bowl. Set aside.
3. Brown sausage in Dutch oven over medium-high heat, breaking up clumps, 5 to 7 minutes. Using slotted spoon, transfer sausage to plate. Add onions and celery to pot and cook until softened, 6 to 8 minutes. Stir in garlic, sage, thyme, salt, and pepper and cook until fragrant, about 1 minute. Transfer to bowl with cornbread. Melt butter in now-empty pot. Add apples and cook until just tender, about 6 minutes. Transfer to bowl with cornbread. Add cherry mixture to cornbread along with remaining 3-1/2 cups broth, egg, and cooked sausage.
4. Transfer mixture to 3-quart baking dish and bake until top is golden brown and crisp, about 25 minutes. Serve.