Sweat the onion in the oil or butter until soft, then add the peas and lettuce. Pour over two-thirds of the stock, bring to the boil and simmer gently for 4-6 minutes (until the fattest of the peas are completely tender).
Remove from the heat and add the lovage leaves or tarragon, then blend the soup with a hand blender or in a liquidiser. I stop blending before it is completely smooth, as I like to see and feel some texture, but a completely smooth, velvety texture is also nice. Thin the soup to your preferred texture with the remaining stock. I like it quite thick, but again, it's a matter of personal taste.
To serve cold, chill in the fridge, or if you're in a hurry, transfer to a cold bowl and place this in a second, larger bowl half filled with iced water. Stir until chilled, changing the water and adding more ice as necessary.
To serve hot, reheat, stirring occasionally and do not allow to boil. In both cases, garnish with a single lovage leaf or a tiny sprig of tarragon in each bowl.
