Step 1

Preheat the oven to 375 degrees F.

Step 2

Place the squash halves cut side up on a baking sheet and brush the insides with 1/2 tablespoon of the olive oil. Sprinkle evenly with 1/4 teaspoon salt, a few turns of black pepper, the cinnamon, paprika, cayenne, and cloves and bake until a fork pokes easily into the center. Begin checking for doneness after 1 hour.

Step 3

Meanwhile, in a large pot, heat the remaining 2 tablespoons olive oil over medium heat. Add the onion and remaining 1/2 teaspoon salt. Cook, stirring, until the onion is soft and translucent, 5 to 7 minutes. Add the garlic and thyme and cook for 2 more minutes. Transfer the mixture to a blender or food processor, add the tomatoes with their juices, and blend until very smooth. Return the mixture to the pot.

Step 4

Scoop the insides out of the squash and place it in the blender with the vegetable broth and blend until very smooth. Add it to the pot, bring it to a boil over high heat, then reduce to a simmer. Simmer, covered, for 20 minutes, stirring occasionally. Taste and adjust seasonings as desired. Ladle into bowls, drizzle with olive oil, and top with grated Parmesan.