Pre-heat oven to 400°F.
Cut squash in half lengthwise and scoop out seeds.
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.
Place in pre-heated oven and roast until squash is very tender when pierced with the tip of a knife; 50 to 55 minutes.
Remove from the oven and let cool slightly; about 15 minutes.
In a 6-quart pot or Dutch oven, heat remaining 2 tablespoons oil over medium heat.
Add shallots and garlic; season with salt and pepper; 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; reduce heat to medium-low and simmer, stirring a few times; 30 minutes.
Remove from heat and let cool 5 minutes.
Working in batches, puree soup in a blender until smooth; alternatively, if an immersion blender is available, leave soup in pot and blend until smooth.
Once blended together, return to pot; heat over medium heat.
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, sprinkled with toasted squash seeds, if desired.
Soup can be stored in an airtight container in refrigerator up to 1 week.