Heat the butter in a large saucepan over medium-low heat. Add the onion, and cook until translucent, about 5 minutes. Add the carrots, and cook until very tender, about 15 minutes. Do not brown. Add the carrot juice, stock, cumin, honey, salt, and white pepper. Bring to a simmer, and cook until vegetables are very soft, about 30 minutes.
Remove from heat, and cool slightly. Puree in batches in a blender or food processor, filling no more than halfway. Return to pan, and warm over low heat, thinning with stock or water if needed. Stir in half-and-half, if using. Garnish with chives and cayenne, and serve.