Tip:Venting the lid of the blender prevents the heat from building up inside, which could cause hot soup to spew out all over the kitchen. Draping a dishtowel over the vented lid guards against splatters.
Heat the butter or oil in a wide soup pot over medium heat. Add the carrots, onion, and shallot and cook, stirring occasionally, until slightly softened, about 6 minutes. Add the garlic, ginger, chile, coriander, curry powder, and a generous pinch of salt. Cook until fragrant, another minute. Pour in the chicken broth, cover partially, and bring to a boil over high heat. Reduce the heat and simmer gently until the vegetables offer no resistance when mashed against the side of the pot with a wooden spoon, 25 to 35 minutes. Remove from the heat.
Ladle some solids and broth into a blender, taking care to fill the jar no more than two-thirds full. Before turning on the blender vent the lid by removing the popout center if there is one, or just open the lid a bit. Drape a clean dishtowel over the vented lid. Purée the soup in batches if needed and then strain through a medium sieve. Stir in the coconut milk and lime juice; season to taste with salt and pepper. Chill thoroughly.
Before serving, thin the soup gradually as needed with up to 1 cup of water and adjust the seasonings. Ladle the soup into bowls or cups. Garnish with a few cilantro leaves and the pepitas or pine nuts.