Melt butter in a large saucepan over medium heat. Add leeks and cook, stirring, until softened, about 10 minutes.
Add potatoes, salt, and broth; simmer until potatoes are tender, about 30 minutes.
Transfer mixture to the jar of a blender or bowl of a food processor; blend until smooth. Set a fine mesh strainer over a large saucepan; strain liquid into saucepan. Add half-and-half, heavy cream, and nutmeg; season with white pepper.
Return to stove and gently heat over medium-high heat until warmed through. Serve garnished with chives.
