Preheat the oven to 375ºF.

Heat the oil in a wide, ovenproof 6 quart pot over moderately high heat and add the star anise and cloves. Cook, stirring, for 30 seconds. Add the chile, fat, bay leaves, garlic, ginger, rosemary, and onion. Cook, stirring, until the onion has softened, about 5 minutes. Add the squash and lime juice, stirring to coat the squash with the lime juice, and season with salt and a generous amount of pepper.

Roast the squash, uncovered, in the middle of the oven, stirring occasionally, until the squash is tender, about 30 minutes. Stir in the maple syrup and salt and pepper to taste. Remove the star anise, cloves, bay leaves, and rosemary before serving.