Cut and discard the root end and thick green parts of your leeks. Slice the leeks in half lengthwise and rinse under cold water, pulling apart layers to remove any grit tucked inside. Once clean, roughly chop the leeks.
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.
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.
Remove the bay leaves, then purée the soup with a hand-held immersion blender until smooth. (Or use a standard blender to purée the soup in batches, taking care not to fill the blender jar more than halfway.) Add the heavy cream and bring to a simmer. If the soup is too thick, add water or stock to thin it out.
Taste and adjust seasoning with salt and pepper. Top with optional chopped chives or crumbled cooked bacon.