Prepare the vegetables. Wash the celery well, then cut it into small slices. Peel and dice the potato, chop the onion finely, and crush the garlic so everything is ready before cooking begins.
Soften the onion. Place a large saucepan over medium heat and melt the 40g butter with the 1 tablespoon olive oil. Add the finely chopped onion and cook gently for about 5 minutes, stopping once it has softened but before it browns.
Cook the celery and garlic. Add the crushed garlic and sliced celery to the softened onion. Continue cooking for another 5 minutes, stirring from time to time, until the celery begins to soften.
Pour in the stock. Add the diced potato, followed by the 1 litre vegetable stock or chicken stock. Stir the contents of the saucepan together and bring the liquid to a gentle boil.
Simmer until tender. Turn down the heat and leave the soup uncovered at a simmer for about 20 minutes. Continue until both the celery and potato are completely tender, which will allow them to blend smoothly.
Blend with the parsley. Take the saucepan off the heat and stir in the 2 tablespoons chopped fresh parsley. Use a stick blender to puree the soup thoroughly until the texture is completely smooth and creamy.
Finish with cream. Put the saucepan back over low heat and stir in the 100ml double cream. Add salt and freshly ground black pepper to taste.
Serve the soup. Spoon the warm soup into bowls. Finish with chopped parsley, freshly cracked black pepper and a small swirl of cream, with crusty bread or toasted baguette slices alongside.