1. Rinse squash. With a large, heavy knife, cut in half lengthwise, using a mallet or hammer gently, if necessary, to force knife through squash. Scoop out and discard seeds. Brush cut surfaces with olive oil. Set squash cut side down in a 10- by 15-inch baking pan.
2. Bake in a 375° regular or convection oven until squash is soft when pressed, 45 to 60 minutes. Reserve pan juices. Scoop flesh from peels (you should have about 5 cups) and discard peels.
3. Meanwhile, trim and discard root ends and tough dark green tops from leeks. Cut leeks in half lengthwise and rinse thoroughly under cold running water, flipping layers to release grit. Chop leeks.
4. In a 5- to 6-quart pan over medium-high heat, stir leeks, garlic, and ginger in butter until leeks begin to brown, 6 to 7 minutes. Add coriander, squash, reserved pan juices, and 5 cups broth. With a potato masher, mash squash. (Soup will be chunky; for a smoother texture, pour it into a large bowl, then purée in a blender, a portion at a time, and return to pan.) Thin with 1 to 4 more cups broth, if desired.
5. Cover and heat soup until steaming. Add salt and pepper to taste. Ladle into bowls and garnish with a dollop of sour cream and a teaspoon or two of chili purée (or a sprinkling of chili powder).