In a large pot, heat 2 tbsp. olive oil over medium. Add the onion; cook, stirring often, until softened, about 5 minutes. Add the carrots and coriander; season with salt and pepper. Cook, stirring often, until the carrots begin to soften, about 5 minutes. Stir in the stock; bring to a boil. Reduce the heat to medium; cover and cook until the carrots are tender, about 15 minutes.
In a skillet, heat the remaining 2 tbsp. oil over medium-high. Add the shrimp, curry powder and cayenne. Cook, turning once, until the shrimp are opaque in the center, about 3 minutes; season.
In a blender, working in batches if necessary, puree soup with 1/4 cup coconut milk; season. Divide among bowls; drizzle with remaining coconut milk. Top with shrimp and chives.
