How to Make It
Cut cilantro leaves and tender stems from tougher stems; set aside leaves and tender stems for serving. Chop a small handful of cilantro stems to reach 1 tablespoon; set aside.
Heat 2 tablespoons oil in a large pot over medium. Add onion, carrot, garlic, chopped cilantro stems, and ½ teaspoon salt and cook until softened, 8 to 10 minutes. Add pumpkin puree, chili powder, and ginger and cook, stirring often, until deepened in color, about 2 minutes.
Add broth and 1½ cups water and bring to a boil. Reduce heat and simmer over medium-low, stirring occasionally, until flavors meld, 15 minutes.
Meanwhile, combine remaining 2 tablespoons oil and shallots in a small skillet and heat on high heat, until shallots are bubbling and starting to darken around the edges, about 2 minutes. Reduce heat to low and continue to cook, until golden brown, 2 to 3 more minutes. Transfer shallots to a paper towel lined plate with a slotted spoon; discard oil. Season shallots with a pinch of salt.
Whisk coconut milk in a medium bowl until thickened and set aside.
Puree soup in a blender until smooth and season with remaining 1 teaspoon salt and freshly ground black pepper. Serve soup in bowls and top with coconut milk, shallots, and cilantro leaves. Serve with lime wedges.