Peel, wash and chop the potatoes. Peel and wash the carrots. Cut about 1/2 carrot into slices. Cut the rest of the carrots into small pieces. Cut the chilli lengthwise, remove seeds, wash and cut into fine rings. Peel and chop onion.
Heat the oil in a large pot. Fry carrots, potatoes, onions and half of the chilli in it. Stir in curry paste and sweat briefly. Add coconut milk, except 4 teaspoons, and 3/4 l water, bring to the boil and stir in the stock. Cover and simmer over medium heat for about 15 minutes.
Wash coriander, shake dry, pluck off leaves. Finely puree the soup with a hand blender. Season to taste with salt, pepper and lime juice. Add carrot slices and cook for 2-3 minutes. Serve the soup. Stir 1 teaspoon of coconut milk into the soup in streaks. Sprinkle with coriander and the rest of the chilli.