Clean the leeks, wash well and chop. Peel and chop the garlic. Heat the butter in a saucepan and saute the leeks and garlic until translucent. Scrub, rinse and peel the potatoes, cut them into pieces and add to the pan.
Pour the broth and cream into the saucepan, bring to a simmer and cook until the potatoes are soft. Stir in the lime juice and nutmeg and season with salt and pepper.
Working in batches, transfer to a blender and puree until smooth. Let cool. Pour into glasses and serve garnished with ice cubes. Serve with pita bread.