Melt half of the butter in saucepan over medium heat. Add the onion and celery and cook and stir until soft, about 10 minutes. Add the stock and bring to the boil. Season with celery salt and pepper. Reduce heat and simmer for 30 minutes.
Melt the remaining butter in a small pan and add the walnuts. Cook and stir until golden and fragrant, about 3 minutes. Set aside.
Blend the soup until smooth using a food processor or a handheld liquidiser. Return to the heat and stir in the cream and toasted walnuts. Serve in warmed bowls garnished with celery leaves.