Step 1Cook bacon in 3 1/2- to 4-quart saucepan or Dutch oven over medium heat until crisp, 4 to 5 minutes. Drain on paper towels and crumble. Set aside and keep warm. Remove all but two tablespoons bacon fat from pan. Addapples to pan and saute over medium heat until tender, about 5 minutes. Use a spoon to scrape flesh from cooked squash and add to pan. Discard skins. Saute until heated, about 2 minutes. Add 1 cup broth and bring mixture to a simmer.
Step 2Puree mixture in blender or work bowl of food processor fitted with metal blade until smooth. Return to saucepan and add remaining broth, cream, nutmeg and sugar. Stir until thoroughly blended. Bring to simmer and cook 10 minutes. Add salt and pepper to taste.
Step 3Ladle soup into warm bowls, garnish with reserved bacon and serve immediately.