Clean, wash and finely dice the leek. Peel garlic, chop finely. Melt butter in a pot. Steam leek and garlic for about 5 minutes. Add wine, lemon peel and juice. Steam for about 7 minutes, stirring occasionally, until the leek is soft. Blend finely with a hand blender and allow to cool.
Wash the chives, shake dry and cut into fine rolls. Stir mascarpone into the leek puree. Season with salt and pepper. Fill the dip into small bowls and sprinkle with chives. Serve with crackers, bread chips or grissini.