Preheat oven to 375ºF; line a large baking sheet with foil. Place squash cut sides up on sheet, sprinkle with salt and pepper and cover with foil. Roast until soft, about 1 hour 15 minutes. Cool slightly, then scoop out flesh with a large spoon. Discard skins.
In a large pot, melt butter over medium heat. Add onion, sprinkle with salt and cook, stirring, until soft, about 8 minutes. Do not allow onions to brown. Peel, core and roughly chop apples. When onion is soft, add garlic and chopped apples to pot and cook, stirring, for 3 minutes. Add pumpkin pie spice; stir for 1 minute. Stir in squash and broth; bring to a boil over high heat. Reduce heat to low and simmer until apples are completely soft, 25 minutes.
Working in batches, puree soup in a blender until smooth. Season with salt and pepper. Return soup to pot and place over low heat to keep warm.
Divide soup among 8 bowls and serve immediately. If desired, drop a dollop of sour cream in the middle of each. I used Gruyere instead of sour cream, and it was delicious. However, the soup really doesn't need anything on top!