Cut squash in half lengthwise; remove seeds. Cover each squash half with microwavable plastic wrap; place on microwavable plate. Microwave on High 8 to 16 minutes or until fork-tender. Cool 10 to 15 minutes before handling.
Meanwhile, in 4-quart Dutch oven, melt butter over medium heat. Add onion and mushrooms; cook about 10 minutes, stirring occasionally, until tender. Stir in garlic, salt, ginger, cumin, black pepper and ground red pepper. Add broth; heat to boiling over high heat. Reduce heat to low; simmer uncovered 5 minutes to blend flavors.
Scoop flesh from cooled squash into blender or food processor. Add half-and-half; blend until smooth. Stir squash mixture into mushroom mixture in Dutch oven. Simmer uncovered 10 minutes longer, stirring occasionally, until thoroughly heated.