Place squash cut side up in two 13-in. x 9-in. baking dishes. Brush insides of squash with butter. Add 1/2-in. of hot water to each dish. Cover and bake at 400° for 35-40 minutes or until squash is tender.
Meanwhile, in a large saucepan, cook the apples, carrot and onion in oil until tender. Add broth; bring to a boil. Reduce heat; cover and simmer for 20 minutes. Stir in the brown sugar, mustard, allspice, ginger and pepper. Cool slightly.
Process in small batches in a blender until smooth. Return to the pan. Add cheese and cream; cook and stir until smooth and blended. Place squash halves on serving plates; fill with soup. Garnish with sour cream and chives.