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 needed to avoid browning.

Add the potatoes, broth, bay leaves, thyme, salt, and pepper. Bring to a boil, then cover and reduce heat to low. Simmer for 15 minutes, or until the potatoes are very soft.

Remove and discard the thyme sprigs and bay leaves. Puree the soup with an immersion blender until smooth, or carefully blend in batches in a countertop blender.

Stir in the heavy cream and return the soup to a gentle simmer. Taste and adjust seasoning with additional salt and pepper if needed. If the soup is too thick, thin with water or broth.

Serve hot, garnished with finely chopped chives if desired.