Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the apple halves, cut sides down, over direct medium heat, with the lid closed as much as possible, until nicely browned and the skins start to pop off, 10 to 15 minutes, turning once. Remove from the grill, let cool, remove the skins, and chop into large pieces.
In a large saucepan over medium heat, warm the butter and sauté the celery, onion, and carrot until the onion is translucent, about 10 minutes. Add the apples and cider. Simmer until the vegetables are soft, 5 to 10 minutes. Stir in the pumpkin and cream; return to a simmer and then add the allspice and nutmeg.
Using a hand blender, puree until smooth (or strain the solids, place the solids in a blender, puree, and add back to the liquid). Heat through. Season with salt and pepper.