Ingredients

1. 4 sugar pumpkins or 2 medium butternut squash (about 5 pounds total), halved and seeded
2. 6 tablespoons extra-virgin olive oil
3. Kosher salt and freshly ground pepper
4. Five 1-pound lobsters
5. 1 stick (4 ounces) unsalted butter
6. 1 large white onion, chopped
7. 2 garlic cloves
8. 1 thyme sprig
9. 1 rosemary sprig
10. 1 bay leaf
11. 1 cup medium-dry white wine
12. 1/2 cup crème fraîche
13. 1 1/2 teaspoons garlic powder
14. 1 1/2 teaspoons onion powder
15. 1 teaspoon cayenne pepper
16. 1 teaspoon dry mustard
17. 1/2 teaspoon ground cumin
18. 1/4 teaspoon freshly grated nutmeg
19. 1/4 teaspoon cinnamon
20. 1/4 teaspoon ground cloves

Directions

1. Preheat the oven to 350°. Drizzle the pumpkin halves with 2 tablespoons of the olive oil and season with salt and pepper. Wrap each half tightly in foil and bake on a large cookie sheet for 1 hour and 15 minutes, or until tender. Let cool slightly, then scoop the pumpkin flesh into a bowl.
2. Meanwhile, bring a stockpot of water to a boil. Prepare a large bowl of ice water. Salt the boiling water and add the lobsters. Cover and cook over high heat for 3 minutes. Using tongs, transfer the lobsters to the ice water and let cool. Twist off the heads and reserve. Crack the claws and remove the meat in 1 piece. Using a heavy knife, halve the lobster tails lengthwise, cutting through the meat and the shells. Remove the dark intestinal veins from the tails. Transfer the lobster tails and the claw meat to a large baking sheet; refrigerate.
3. Clean out the lobster heads with a spoon and return the shells to the stockpot. Simmer the shells for 30 minutes, skimming frequently. Strain the lobster stock through a fine sieve and reserve 8 cups.
4. In a soup pot, melt 4 tablespoons of the butter. Add the onion, garlic, thyme, rosemary and bay leaf. Cook over moderate heat, stirring occasionally, until the onion is softened, about 8 minutes. Add the cooked pumpkin and the wine and simmer until the wine has reduced by half, about 5 minutes. Add 6 cups of the lobster stock and simmer for 30 minutes. Remove and discard the herb sprigs and bay leaf.
5. In a food processor or blender, puree the soup with the crème fraîche. Return it to a clean pot. Add enough of the remaining 2 cups of lobster stock to make the soup velvety; season with salt and pepper.
6. Mix 1 tablespoon of kosher salt with 2 teaspoons of pepper and the garlic powder, onion powder, cayenne, dry mustard, cumin, nutmeg, cinnamon and cloves.
7. In a very large skillet, heat the remaining 1/4 cup of olive oil. Add the lobster tails, cut sides down, and cook over high heat until the shells begins to brown, 3 minutes. Reduce the heat to moderate, turn the tails and add the remaining 4 tablespoons of butter and the spice mixture. Cook the tails for 2 minutes, basting them with the spice butter. Transfer the tails to a plate and remove the meat from the shells. Add the lobster claws to the skillet and baste with the spice butter, 2 minutes per side. Add the claws to the tails on the plate.
8. Bring the soup to a simmer. Ladle into warmed bowls and garnish each serving with a lobster tail half and a claw.

Make Ahead

The soup and lobster can be prepared through Step 6 and refrigerated for up to 2 days.