Fresh pumpkin lends this soup a particularly pronounced flavor; for a more refined presentation, strain the pumpkin purée just before adding the spices.
*Note: You can substitute ½ teaspoon dried sage for every 1 ½ teaspoons fresh sage.
Preheat the oven to 350 degrees. Coat a large baking sheet with cooking spray.
Cut the pumpkin in half through its “equator” (meaning horizontally and not through the stem). Scoop out any seeds and fibrous membranes. Set the pumpkin halves cut side down on prepared tray. Place a garlic clove under each pumpkin half. Bake until the pumpkin is soft and tender, about 1 hour. Let cool for 20 minutes. (At this point, the pumpkins can be put in a large, sealable container and stored in the refrigerator for up to 3 days.)
Scoop the flesh from the pumpkin shells into a food processor fitted with the chopping blade or a large blender. Add the garlic cloves and 2 cups of the broth; process or blend until smooth, scraping down the insides of the canister as necessary.
Pour the pumpkin purée into a large saucepan; stir in the remaining broth, sage, salt, allspice, and cinnamon. Bring to a simmer over medium-high heat, stirring occasionally. Reduce the heat to low and simmer, uncovered, for 10 minutes for flavors to blend.