1. Cut the leek in quarters lengthwise and wash thoroughly. Wash the lettuce well. Grind both in a food chopper, using the finest knife.
2. Heat the butter, add the leeks and lettuce and saute until soft but not browned. Add the broth, peas and seasonings and cook until the peas are very tender. Strain the broth and rub the vegetables through a sieve or food mill, or puree in a blender. Chill thoroughly.
3. At serving time, fold in the whipped cream and serve garnished with chopped chives.