1. Heat the oil over medium heat in a 6-quart stockpot. Add the onion and cook until soft but not brown, about 6 minutes. Add the garlic, allspice and ginger, and cook, stirring frequently, for 1 minute more.
2. Add the squash, broth and salt, and bring to a boil. Reduce heat and simmer until squash is tender and the broth is slightly reduced, about 15 minutes for fresh squash and 5 minutes for frozen. Remove from heat and stir in maple syrup. Allow soup to cool slightly, then puree in a blender until smooth.