Thoroughly wash the leeks, then thinly slice them into rounds.
Peel the potatoes and cut them into small cubes.
In a saucepan, melt the butter over medium heat and sauté the leeks for 5 minutes, or until softened.
Add the potatoes, then pour in the vegetable broth and cook over medium heat for about 20 minutes, or until the vegetables are completely tender.
Use an immersion blender to purée the soup until completely smooth.
Stir in the heavy cream, then season with salt, pepper, and nutmeg. Mix well and simmer for another 2-3 minutes.
Before serving, let it cool slightly, then garnish with fresh chives or toasted bread croutons.
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