Melt the butter in a large pot over medium-high heat. Add the leeks, ginger, and garlic and cook until the leeks are soft, about 5 to 6 minutes. Add the carrots, allspice, and cinnamon and stir well to combine. Add the stock and water, raise the heat to high, and bring it to a boil.
Turn the heat down and simmer until the carrots are soft, about 10 to 12 minutes. Skim off any foam that may form. Purée the soup in batches in a blender. Return the soup to the heat and stir in the honey. Taste and adjust the seasoning with salt and pepper. Serve garnished with chopped chives.