Place the butter in a large, deep pot over medium-high heat. When the butter is melted, add the leeks and potatoes, sprinkle with salt and pepper, and cook until the veggies start to soften, 5-8 minutes.
Add the water and bring to a boil. Then, lower the heat so the soup bubbles gently and cook, stirring occasionally, until slightly thickened and vegetables become fully tender, about 20 minutes longer.
Using an immersion blender, puree the soup in the pan; or let the mixture cool slightly and use a blender to process until smooth. Return the soup to the pan and add the cream; taste and adjust the seasoning. Serve garnished with chives.