Preheat the oven to 400˚F. Line a baking sheet with parchment paper.
Cut the squash in half lengthwise. Spoon out and discard the seeds. Drizzle the squash flesh lightly with olive oil, then place the halves, cut sides down, on the prepared baking sheet. Bake until the flesh is tender when pierced with a small knife, 45 minutes-1 hour. Let cool, then scoop out the flesh (you should have roughly 4 cups). Do Ahead: The cooked squash can be refrigerated for up to 5 days.
In a large saucepan, heat the coconut oil over medium-low heat. Add the leeks, ginger and serrano chile, and season with salt and pepper. Cook, stirring occasionally, 8-10 minutes, or until the leeks are tender but not browned. Add the curry powder, cinnamon and allspice, and cook until fragrant, about 1 minute. Stir in the cooked squash and brown sugar, and season with salt and pepper. Pour in the coconut milk and water. Stir, breaking up any large chunks of squash with a wooden spoon. Increase the heat to medium-high and bring to a boil. Reduce the heat to a simmer and cook, covered, 20 minutes.
Working in batches, puree the soup using a blender or hand blender. Pour the pureed soup into a clean saucepan. If the soup is too thick, thin it with water. Squeeze in the lime juice, and season with salt and pepper to taste. Cook until warmed through.
Ladle the soup into serving bowls. If you'd like, drizzle the soup with coconut cream and garnish with cilantro leaves and toasted coconut flakes.