Heat the oil in a saucepan. Add the onion, carrot, garlic, leek, celery, parsley, potato and ham. Stir well, then cover the pan, reduce the heat and sweat the vegetables for about 30 minutes or until they are softened. Stir the vegetables occasionally so that they cook evenly.
Add the peas, herbes de Provence and stock. Bring to the boil, then reduce the heat to medium–high and cook until the peas are just tender – allow about 10 minutes for fresh peas or 5 minutes for frozen. Add the lettuce and cook gently for a further 5 minutes.
Purée half to two-thirds of the soup in a blender, then stir the purée back into the rest of the soup. Alternatively, use a hand-held blender to partly purée the soup in the pan. Reheat the soup gently, if necessary, then taste and adjust the seasoning. Ladle the soup into warm bowls. Swirl a little cream into each portion and serve at once.