Melt the butter over medium heat in a dutch oven.
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 the pot and bring to a boil.
Reduce heat to medium-low and simmer for 15 minutes, or until the potatoes are very soft.
Fish out the thyme sprig and bay leaves, then purée the soup with a hand-held immersion blender until smooth.
Add the heavy cream and bring to a simmer.
Taste and adjust seasoning with salt and pepper.
If the soup is too thin, simmer until thickened. If it's too thick, add water or stock to thin it out.