For the soup: Drain the water from the wood chips.
Prepare the grill for indirect heat: If using a charcoal grill, light the coals. When the coals are hot, scatter the wood chips directly onto them. If using a gas grill, place 1 cup of the drained chips in a smoker box or an aluminum foil pouch punctured on top with a fork to release smoke. Place the smoker box or foil pouch between the grate and briquettes, close to the flame. Preheat on high until you see smoke, then reduce the heat to medium (350 degrees).
Meanwhile, discard the pumpkin stem. Cut the pumpkin in half from top to bottom. Scrape out all of the seeds and fiber.
When ready to grill, place the unpeeled pumpkin halves, flesh sides down, on the far side of the grill, away from the coals or flame. Smoke the pumpkin for 60 to 90 minutes, until a fork slides easily through the flesh.
Remove the pumpkin from the grill. When cool enough to handle, use a spoon to scrape the pumpkin flesh from its skin into a bowl. Discard the skin.
Melt the butter in a large pot over low heat. Add the shallot and cook for about 5 minutes, until soft. Add the broth, cinnamon, allspice and orange juice. Increase the heat to medium-high and bring to a boil, then reduce the heat to medium-low. Stir in the pumpkin; cook for 10 minutes, then add the cream and nutmeg, stirring to incorporate. Turn off the heat. Let cool for about 20 minutes.
Working in batches, transfer the soup to a food processor. Puree until smooth, then strain into a clean pot. Place over low heat and keep warm. Season with the salt and pepper.
For the rum cream: Pour the cream into the bowl of a stand mixer or hand-held electric mixer. Beat on medium speed until soft peaks form. Add the lemon zest and juice, rum and sugar. Continue whipping until the cream is almost stiff. Cover and refrigerate until ready to serve.
Divide the soup among individual bowls; top each portion with equal amounts of the rum cream. Serve right away.