Preheat the oven to 400°F.

Cut the squash into 1-inch cubes. Cut the onion and carrot into 1/2-inch pieces, and smash the garlic clove.

Heat the oil in a large oven-safe pot or Dutch oven over medium-high heat. Once oil is shimmering, add onion, carrot, and garlic. Cook, stirring frequently, until vegetables are lightly golden, 5-6 minutes.

Turn off heat and add the squash, nutmeg, cinnamon, cayenne, salt, black pepper, broth, and maple syrup to the onion mixture. Stir briefly to combine. Cover the pot tightly with a lid.

Bake the soup mixture on middle rack of oven until vegetables are very tender, 45-60 minutes.

Check to see that vegetables are done. Remove from oven or add time as needed.

Remove lid and allow the soup to cool for 10 minutes.

Transfer contents of the pot to the bowl of a food processor. Process on high until the soup is completely smooth. Alternately, the soup may be pureed using a blender or an immersion blender. Add additional broth to thin the soup, if necessary. Season with additional salt and black pepper, if desired.

Pour the soup into bowls and serve.