Slice the white part of the leeks and chop the onion.

Melt butter in a large pot over medium heat.

Sauté the leeks and onion in butter until softened and yellow, about 5-7 minutes.

Peel and cube the baking potatoes.

Dice the carrot.

Add potatoes, carrot, chicken stock, and salt to the pot.

Bring the mixture to a rapid boil.

Reduce the heat to low, cover, and simmer until the potatoes and carrots are soft, about 20-25 minutes.

Mash the soup with a potato masher.

Rub the soup through a fine sieve or use an immersion blender to puree until smooth.

Return the soup to the pot.

Add milk and season to taste with salt and pepper.

Cool the soup to room temperature.

Stir in the cream and chill thoroughly in the refrigerator for at least 1 hour.

Serve cold with a sprinkling of finely chopped chives.