Chop the leeks, using the white and light green parts only. Peel the potatoes, cut into chunks, and set aside in a bowl of water to prevent oxidation.

Melt the butter in a heavy pot. Add chopped leeks, season with salt and pepper, and cook until softened.

Add the stock and potatoes, and simmer until potatoes are soft.

Blend until perfectly smooth in a high-powered blender, such as a Vitamix.

Return to the pot, and whisk in the heavy cream.

Taste the soup and correct the seasoning. Divide among serving bowls, and garnish with chives if desired.