1. Preheat oven to 400°.
2. Cut squash in half lengthwise and remove seeds. Drizzle halves liberally with oil and season with salt and pepper. Place on parchment-lined baking sheet and roast until soft and beginning to brown in spots, about 45 minutes. When cool to the touch, scoop out flesh with a spoon.
3. Place roasted squash flesh in a large soup pot and add chicken stock. Bring to a boil and then blend until smooth with an immersion blender. Add more stock as necessary to reach desired consistency. Add kale and beans and simmer until kale is tender, 5–10 minutes. Serve hot topped with grated parmesan and a thick slice of crusty bread for dunking.