Preheat oven to 350 degrees F. If using Sweet Mama, use half to three-fourths of the squash. If using butternut or acorn squash, cut in half lengthwise; remove and discard seeds. Arrange squash, cut sides down, in 3-quart rectangular baking dish. Bake for 1 to 1-1/4 hours for Sweet Mama, 45 to 60 minutes for butternut or acorn, or until squash is tender. Remove from oven; cool slightly. Scoop pulp from squash halves. Place cooked pulp in a bowl; mash with a potato masher or fork (you should have about 2 cups pulp).
Meanwhile, in a saucepan cook onion in hot oil for 5 minutes or until onion is tender. Stir in broth, apples, and maple syrup. Bring to boiling, reduce heat. Simmer, covered, for 20 minutes or until apple is very tender. Remove from heat. Cool slightly. Stir in mashed squash.
Transfer half the squash mixture to a blender container or one-fourth the squash mixture to a food processor bowl. Cover; blend or process until smooth. Repeat with remaining mixture.
Return blended squash mixture to saucepan. Stir in whipping cream (if necessary, add additional broth to make desired consistency); heat through. Season to taste with salt and pepper. Sprinkle each serving with chopped apple. Makes 8 side-dish servings.