Potatoes and leeks are a classic combination, traditionally paired in vichyssoise, a cold French soup. Here the duo has been enlivened with the delicate, yet peppery bite of watercress, and the soup is served hot. For an elegant presentation, puree the soup base. The soup is equally delicious served chunky, just be sure to cut the potato cubes so they are bite-sized. Any baking potato can be used, but I'm partial to Yukon Golds because of their creamy, buttery taste.
Place the butter in a large saucepan or stockpot and melt over medium heat. Add the leeks and cook, stirring frequently, until the leeks are soft, about 5 minutes.
Add the chicken stock and the potatoes to the pan and bring the soup to a boil. Lower the heat to medium, cover the pan, and cook until the potatoes are very tender, about 30 minutes.
Add the half and half and the watercress and stir until the cress is wilted, about 5 minutes.
If desired, puree in batches in a food mill or use an immersion (stick) blender. Season to taste with salt and pepper, if needed.