In my opinion, live juice would be the very best way to break the fast, i am rather partial to pinapple juice myself :). You could satisfy your carrot craving with carrot juice (and i would recommend that you water it down 50%).
I also believe that cooking up vegetable juice into a broth would be fine as long as you nourish yourself primarily with the live juices. In my current juice fast, i am drinking a broth made from tomato, carrot, asparagas, celery, bok choy, onion and garlic, sprinkled with some cayanne pepper, red pepper and indian curry... even as i type this.