1. For the Lobster Broth, remove all lobster meat. Cut lobster meat into 3/4-inch dice; transfer to small bowl, cover and refrigerate. You should have about 2-1/2 cups. With sharp knife, split lobster carcasses (shells) in half. Remove head sack (it can cause bitterness). Combine lobster carcasses, chicken broth, and water in a large Dutch oven. Bring to boil over medium-high heat. Skim any foam from top.
2. Remove kernels from corncobs (you should have 2 cups); set aside. Break corncobs in half, add to broth with thyme, bay leaf, and peppercorns. Reduce heat to medium and simmer broth, partially covered, 1 hour. Strain broth into a large bowl. Discard shells, corncobs, and herbs.
3. Melt butter in a 4-quart Dutch oven or soup pot over medium heat. Add onions and cook, stirring, until softened and golden, 8 minutes. Stir in reserved lobster broth, corn kernels, pumpkin, and nutmeg. Simmer mixture until pumpkin is very tender, 30 to 45 minutes.
4. Puree soup in batches in blender or food processor. Strain mixture through a sieve into a medium saucepan and reheat over medium-low heat. Stir in cream, kosher salt, pepper, and ground red pepper. Gently warm soup 5 minutes. Add reserved lobster meat and cook until lobster is just heated through, about 1 to 2 minutes. Divide soup among 8 shallow serving bowls and sprinkle with parsley. Makes 8 servings.