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. Puree 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.

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.