Heat the butter and 1 tablespoon of olive oil in a large soup pot over medium-high heat. Add the leeks and onions and sauté until soft, about 4 minutes.
Turn the heat down to medium and add the potatoes, stock, and wine. Cover and simmer until the vegetables are tender, about 15 minutes. Remove from heat.
In a medium-sized skillet, heat the remaining 2 tablespoons of olive oil over medium-high heat. Add the chanterelles, turn the heat down to medium, and cook, stirring frequently, until the mushrooms give up their water and the water evaporates, about 10 minutes.
Remove half of the leeks and potatoes from the soup pot and reserve in a bowl.
Puree the remaining vegetables until very smooth, either by using an immersion blender or by pureeing in batches in a standing blender.
Return the puree and reserved vegetables to the soup pot and add the mushrooms. Over low heat, stir in the cream and season with salt and white pepper to taste.
Serve at room temperature or chilled, garnished with chives.
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