Cut off the dark tops and root ends. Slice the white and pale green parts, then swish them in a bowl of cool water so grit falls away. Lift them out, rinse again if needed and drain.

Melt the butter in a large heavy saucepan over medium-low heat. Add the leeks and onion. Cook 8–10 minutes, stirring, until soft but not browned.

Add potatoes, broth, salt and white pepper. Bring to a gentle simmer, cover partly and cook 18–22 minutes, until a potato piece crushes easily with a fork. Remove from the heat.

Blend in the saucepan with an immersion blender only until smooth. For a countertop blender, work in small batches, vent the lid and handle the hot soup carefully. Avoid prolonged blending, which can make potatoes gluey. Stir in the cream. Taste, then adjust the salt.

Transfer the soup to shallow containers and let the steam subside briefly. Refrigerate within 2 hours of cooking, covered at 40°F (4°C) or below, until fully cold, about 4 hours. The soup will thicken; whisk in a little cold broth only if needed.

Stir gently, ladle into six small bowls and scatter with the chopped chives. Serve chilled.