Preheat the oven to 375°F and grease an 8x8 inch baking dish with a little of the melted butter.
In a large skillet over medium heat, cook the sausage until browned and cooked through, breaking it into small pieces as it cooks. Remove the sausage to a large mixing bowl and leave the drippings in the skillet.
Add the onion and celery to the skillet and cook for 4 minutes until softened. Add the diced apples and cook 2 minutes more until the apples begin to soften.
Transfer the vegetable and apple mixture to the bowl with the sausage. Add the crumbled cornbread, sage, salt, and pepper.
In a small bowl, whisk the eggs with the chicken broth. Pour this mixture over the cornbread blend and stir gently until everything is evenly moistened.
Spread the mixture into the prepared baking dish and drizzle the remaining melted butter over the top.
Bake for 30 minutes until the top is golden and the center is set. Let it rest 5 minutes before serving.