Preheat the oven to 400 degrees F (200 degrees C).
Place butternut squash on a rimmed baking sheet and drizzle with 1 tablespoon olive oil.
Roast squash in the preheated oven until tender, 25 to 30 minutes, turning once using a metal spatula. Remove from the oven and set aside.
Heat 2 teaspoons olive oil in a large, deep saute pan over medium-high heat. Saute carrots, onion, celery, leek, and garlic in the hot oil until almost tender, about 5 minutes. Add roasted butternut squash, sage, butter, and thyme and continue to saute until vegetables are tender, 3 to 4 minutes more.
Stir chicken broth into the pan until well mixed with vegetables. Add cornbread stuffing and mix. Add additional chicken broth if necessary and mix until desired consistency is reached. Season with salt and pepper. Set aside and let cool, 10 to 15 minutes. Mix in apple.
Bake/toast cornbread first if making your own croutons instead of using stuffing mix.
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