Drain the peas into a colander. Heat the butter in a large saucepan, add the bacon and onion and fry for 5 minutes until softened. Add the carrot and celery and fry for 5 more minutes, stirring until golden.
Add the peas and stock and bring to the boil, stirring. Boil rapidly for 10 minutes then reduce the heat, cover and simmer for about 1 hour or until the peas are tender.
Allow the soup to cool slightly then purée half the soup in batches in a blender or food processor until smooth. Return to the saucepan and reheat. Add salt and pepper to taste.
Ladle the soup into bowls then sprinkle the parsley and bacon over the top.