In a large saucepan, heat the oil until shimmering. Add the carrots, cilantro stems, lime zest, half of the chilies, half of the shallot, the coriander and 1 teaspoon salt. Cook, stirring, until the shallot is translucent, 2 to 4 minutes. Add 5 cups water and bring to a boil, then cook, uncovered and stirring occasionally, until the carrots are tender. Meanwhile, in a small bowl, stir together the remaining chili, the remaining shallot, the cilantro leaves and lime juice; season with salt and pepper, then set aside until ready to serve. Using a blender, puree in batches until smooth, then return to the pan. Thin to desired consistency with water, then season with salt and pepper. Ladle into bowls, top with the cilantro mixture and a drizzle with additional oil.