Chop leeks and in a bowl of cold water wash leeks well. Lift leeks from water into a colander to drain. In a large saucepan cook leeks in oil with salt and pepper, to taste, over moderately low heat, stirring, until softened. Peel potatoes and cut into 1-inch cubes. Add potatoes, broth, and 2 cups water to leeks and simmer, covered, about 10 minutes, or until potato is tender. Stir in peas and simmer, uncovered, about 5 minutes, or until peas are tender.
While potato mixture is simmering, discard sorrel stems. Cut leaves crosswise into thin strips (about 6 cups loosely packed). In a blender puree potato mixture with sorrel in 4 batches until very smooth, transferring to a bowl. Whisk in yogurt and 1 cup water, adding enough water to thin soup to desired consistency.
Just before serving, stir in lemon juice and salt and pepper to taste. Garnish soup with egg and sorrel.