Melt the butter or margarine in a large saucepan and cook the celeriac and apples over a moderate heat for 5 minutes or until they have begun to soften.
Add the stock and cayenne pepper and bring to the boil. Reduce the heat, cover the pan and simmer for 15–20 minutes or until the celeriac and apples are very soft.
Purée the mixture in a blender or food processor until it is very smooth, transferring each batch to a clean saucepan. Alternatively, rub through a fine sieve. Reheat gently. Season to taste and serve in individual bowls, garnished with the finely diced apple and a dusting of paprika.