Trim the base of the leeks and cut the green tops down to about
Shred the leeks finely, peel the carrots and slice thinly.
Melt the butter in a large saucepan and add the prepared vegetables. Cover and cook gently for about 5 minutes, until the leeks are soft but not browned. Stir in the hot stock and season with salt and pepper. Bring up to the boil, cover with a lid and cook gently for about 1–1½ hours or until the carrots are quite tender.
Draw off the heat and pass the vegetables and liquid through a vegetable mill or purée in a blender. Return the soup to the pan.
Check seasoning and reheat. Stir in the cream and serve.