Cut squash in half crosswise; remove seeds. Place squash, cut side down, in a greased shallow baking dish. Bake at 400° for 45 minutes or until tender; cool. Scoop out pulp, discarding shells.
Sauté onion in butter in a Dutch oven over medium-high heat 7 to 8 minutes or until lightly browned. Add brown sugar; cook 2 minutes, stirring often. Add squash pulp; cook 5 minutes, stirring often. Add broth and next 4 ingredients. Cover, reduce heat to medium-low, and simmer 5 minutes. Remove from heat; cool slightly.
Process soup, in batches, in a food processor or blender until smooth. Return soup to Dutch oven; simmer 5 minutes. Drizzle each serving with a little whipping cream.