Preheat oven to 400 degrees. Cut squash in half lengthwise and scoop out seeds; reserve, if desired (see Cook's Note). Drizzle cut side of squash with 1 tablespoon oil and season with salt and pepper. Place, cut-side down, on a foil-lined rimmed baking sheet. Roast until squash is very tender when pierced with the tip of a knife, 50 to 55 minutes. Let cool slightly, about 15 minutes.

In a 6-quart pot or Dutch oven, heat remaining 2 tablespoons oil over medium. Add shallots and garlic, season with salt and pepper, and cook until shallots are soft and translucent, 6 to 8 minutes. Add ginger and coriander; cook until very fragrant, 2 minutes. Stir in broth, 1 cup water, and 1 teaspoon salt. Scoop flesh from cooled squash into pot. Bring to a boil, then reduce heat to medium-low and simmer, stirring a few times, 30 minutes. Let cool 5 minutes.

Working in batches, puree soup in a blender until smooth. Return to pot; heat over medium. Whisk in coconut milk. Cook until warmed through, 5 minutes. Remove from heat and stir in lime juice. Season to taste with salt and pepper. Serve, drizzled with more coconut milk and sprinkled with toasted squash seeds, if desired. Soup can be stored in an airtight container in refrigerator up to 1 week.