Slice the leek whites and rinse under cold running water.
Heat a slow cooker over low heat until medium. Stir in the butter, leeks, 3/4 teaspoon salt, and 1/4 teaspoon white pepper and cook, stirring occasionally until the leek is translucent, about 5 minutes. Stir in the stock, potatoes, and nutmeg and cook until the potatoes are falling apart, about 6 hours. Stir in the cream.
In a blender, puree the soup, in batches if necessary, until very smooth. Season the soup with salt and pepper to taste and serve, hot or cold, topped with the chives.
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