Place whole squashes in a roasting pan. Bake at 425° for 30 minutes or until just tender. Let stand for 15 minutes. Halve squashes. Scoop out seeds; discard.
Preheat broiler to high.
Heat a large skillet over medium-high heat. Add Italian sausage to pan; sauté 5 minutes or until browned, stirring to crumble. Remove sausage from pan; drain on paper towels. Wipe drippings from pan with a paper towel.
Return pan to medium-high heat. Add oil; swirl to coat. Add onion; sauté 4 minutes, stirring occasionally. Add celery; sauté 3 minutes, stirring occasionally. Add garlic; sauté 1 minute, stirring constantly. Stir in sausage, rice, and next 5 ingredients (through Parmesan). Divide rice mixture evenly among squash halves. Sprinkle evenly with Swiss cheese. Arrange squash halves on a baking sheet; broil 4 minutes or until golden and cheese is melted.