In a large pot, melt the butter over medium heat. Add the leeks and garlic and sauté until the leeks are very soft, about 10 minutes.
Add the potatoes, broth, thyme, bay leaves, salt, and pepper. Bring to a boil. Reduce the heat and simmer until the potatoes are very soft, about 15 minutes.
Remove and discard the thyme sprigs and bay leaves. Working in batches, purée the soup in a blender until smooth. Return to the pot and stir in the cream. Place over low heat for a few minutes to reheat, if needed. Serve garnished with chives and black pepper.
