How to Make It
Spread cubed cornbread on 2 rimmed baking sheets. Place in oven, and preheat to 400°F. Bake until cornbread is golden brown, about 15 minutes after oven preheats.
Heat a large nonstick skillet over high. Cook sausage, stirring occasionally, until browned, about 6 minutes. Transfer sausage to a large bowl, reserving drippings in skillet. Add fennel, 1 tablespoon of the butter, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper to skillet. Reduce heat to medium-high; cook, stirring occasionally, until fennel is tender and slightly browned, about 8 minutes. Add fennel to bowl with sausage.
Add onion, celery, garlic, 1 tablespoon of the butter, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper to skillet; cook, stirring occasionally, until tender, 12 to 15 minutes. Add to bowl with fennel and sausage. Add apple, thyme, and 1 tablespoon of the butter to skillet; cook, stirring often, until apples are slightly browned, 8 to 10 minutes. Add apple mixture and toasted cornbread to sausage mixture in bowl.
Whisk together chicken broth, eggs, and remaining 2 teaspoons salt and 1 teaspoon pepper. Pour over cornbread mixture in bowl, and toss gently to combine. Let stand 10 minutes.
Grease a 13- x 9-inch baking dish with 1 tablespoon of the butter. Spread cornbread mixture in prepared dish. Cover with aluminum foil, and bake in preheated oven 30 minutes. Remove foil; dot dressing with remaining 2 tablespoons butter. Return to oven; bake until golden brown, 25 minutes. Drizzle with maple syrup before serving.