Halve squash and remove seeds. Place squash halves, cut sides down, in a large shallow roasting pan. Bake in a 350 degree F. oven for 50 to 55 minutes or until squash is tender.
Scoop squash pulp out of the peel using a spoon; discard peel. Place pulp, one-third at a time, in a blender container or food processor bowl. Cover and blend or process until squash is smooth, adding some of the chicken broth if the mixture is too thick.
Stir together pureed squash and remaining chicken both in a large saucepan. Stir in ginger, salt, pepper, and cinnamon. Bring mixture to boiling. Reduce heat and stir in half-and-half or light cream. Heat through, but do not boil. If desired, garnish each serving with sour cream and thyme sprigs. Makes 12 side-dish servings.