Melt the butter in a 4-quart pot over medium-low heat. Add the leek and a pinch of salt and cook until tender but not brown, 5 to 7 minutes. Stir in the potatoes and then add 3 cups of water, the broth, and 1 tsp. salt. Bring to a boil, cover partially, reduce the heat to maintain a simmer, and cook until the potatoes are tender, about 12 minutes. Add the sorrel and cook until wilted, 1 to 2 minutes. Remove from the heat and let cool slightly.
Purée the soup in a blender until smooth. Pour the soup into a medium bowl, cover, and refrigerate until completely chilled, about 4 hours. Whisk the yogurt into the soup and season to taste with salt and pepper. Serve garnished with thinly sliced or chopped sorrel leaves.
nutrition information (per serving):
Photo: Scott Phillips; Food styling: Samantha Seneviratne