In a large heavy pot over medium-high heat, add remaining 2 tablespoons of olive oil, onion, carrot, and then season with a pinch of salt. Saute until tender, about 10 minutes. Add garlic and ginger, and sauté for 2 more minutes. Scoop squash flesh into the pot and stir. Add 4 cups vegetable broth and bring to a boil. Reduce heat to low, cover the pot, and simmer vegetables until tender, about 30 minutes.