From The Kitchn
4 to 4 1/2 pounds red Kuri squash
2 tablespoons vegetable oil or butter
4 cloves garlic
4 small shallots
1 tablespoon fresh grated ginger, from a 3-inch long piece
2 tablespoons tomato paste
1 teaspoon curry powder
1 dried red chili, about 2 inches long
1 (13.5-ounce) can coconut milk
4 cups chicken or vegetable broth
1 1/2 teaspoons salt
Juice of 1 lime (about 2 tablespoons)
Heat the oven to 400°F. Use a heavy, sharp knife or cleaver to cut the squash into quarters. Place these quarters in a roasting pan and bake for 1 hour. (Alternate method: Place each squash directly in the oven, whole. Bake for 20 minutes or until soft enough to cut in half with little effort. Cut in quarters, place in a baking dish, and roast for 40 more minutes or until the skin can be easily peeled away from the flesh.)
Put the squash aside for 15 minutes or until it is cool enough to be easily handled. When cool, peel the skin away from the squash flesh. You should have about 3 packed cups of roasted squash.
In a 4-quart or larger pot or Dutch oven, heat the oil or butter over medium heat. When the oil is hot, add the garlic, shallots, and ginger, and fry in the oil for about a minute. Add the tomato paste and fry for another minute. Turn the heat down and cook for about 5 minutes, or until the shallots are beginning to really soften. Add the curry powder and crumble in the red chili. Fry for another minute, then add the squash. Turn the heat back up to medium and fry the squash with the aromatics for about 5 minutes, stirring occasionally.
Stir in the coconut milk and chicken broth and bring to a light simmer. Lower the heat and cover the pot. Simmer for 30 minutes.
Turn off the heat and puree the soup with a hand blender, or pour the soup in batches into a blender and carefully puree it there, holding the top down with a towel. Add the salt in 1/2-teaspoon increments, tasting as you go, and stir in the juice of the lime. Serve immediately.