The most common leek soups combine leeks, potatoes, broth, cream and seasonings and then blend them to a smooth texture. Other variations use coconut milk to give the soup a creamy consistency.
To make potato leek soup, a recipe on FoodNetwork.com suggests cooking chopped leeks in butter over medium heat until they are tender. Add potatoes and butter and allow the combination to simmer approximately 45 minutes. Puree the mixture, then add cream, buttermilk and white pepper. Serve the soup warm or cold, topped with chives.
OnceUponAChef.com offers a variation that incorporates more spices, including garlic and bay leaves. After cooking the leeks with garlic and butter, add potatoes, broth, thyme, bay leaves and seasonings. Cook the mixture for 15 minutes, then remove the whole herbs. Blend the soup, then add cream. The recipe suggests serving the soup with fresh herbs as a garnish.
StupidEasyPaleo.com provides a version of leek soup appropriate for the Paleo diet. For this recipe, simply combine leeks, cauliflower, onions, broth and coconut milk in a pot and allow the mixture to simmer for 20 minutes. Once the soup is cool, blend it and season it with salt and pepper. The site offers instructions for making this dish in a slow cooker as well.