Melt the butter over medium heat in a large soup pot. Add the leeks and garlic and cook, stirring regularly, until soft and wilted, about 10 minutes. Adjust the heat as necessary so as not to brown.
Add the potatoes, broth, bay leaves, thyme, salt and pepper to pot and bring to a boil. Cover and turn the heat down to low. Simmer for 15 minutes, or until the potatoes are very soft.
Fish out the bay leaves, then purée the soup with a hand-held immersion blender until smooth. (Alternatively, use a standard blender to purée the soup in batches; see note.) Add the heavy cream and bring to a simmer. Taste and adjust seasoning with salt and pepper. If soup is too thin, simmer until thickened. If it's too thick, add water or stock to thin it out. Garnish with fresh herbs if desired.
Servings 6
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.
Freezer-Friendly Instructions: The soup can be frozen, without the cream, for up to 3 months. Defrost the soup in the refrigerator for 12 hours and then reheat it on the stovetop over medium heat until hot. Once heated through, add the cream and bring to a simmer before serving.