Heat oil in a large pot over high heat. Add carrots, sweet potatoes, onion and 1 teaspoon salt and cook until onions are softened, about 5 minutes.
Stir in curry powder, jalapeño and ¼ cup cilantro. Cook until fragrant, 2–3 minutes.
Stir in broth, bring to a boil then reduce to a simmer and cook, partially covered, until vegetables are very soft, about 20 minutes.
Meanwhile, in a mortar and pestle, crush together peanuts, 2 tablespoons cilantro, lime zest and ¼ teaspoon each salt and pepper until a chunky paste is formed.
Remove soup from heat and purée using either a standard blender or immersion blender.
Return soup to pot (if using blender) and stir in coconut milk (or milk of choice), lime juice and sugar; season to taste with additional salt.
Top each serving with peanut-cilantro paste and enjoy.