How to Make It
Melt the butter in a medium pot over medium heat. Add the leeks and ½ teaspoon salt. Cook, stirring occasionally, until tender, 4 to 6 minutes.
Add the potato, broth, and 4 cups water and bring to a boil. Reduce heat and simmer until the potato is tender, 8 to 10 minutes. Add the watercress and tarragon. Cook until the watercress is bright green, about 1 minute.
Working in batches, puree the soup in a blender. Add the buttermilk and ½ teaspoon salt and pulse to combine. Serve topped with tarragon leaves.