Boil the carrot or apple juice in a wide pot over medium-high heat, until reduced to 1/3 cup, about 25 minutes (if you don't have carrot juice, see below.*) Let the juice cool, then whisk in the remaining dressing ingredients. If you like, you can wilt the tat soi by steaming or microwaving for a minute or two, with just the water that clings to the leaves after washing. Arrange with the radishes and green onion, and drizzle with carrot dressing. 

*To make carrot juice without a juicer, you can chop and boil a few carrots until they are tender, then puree them with enough water to get a smooth texture. Then you can squeeze the puree through a clean flour sack type dish towel. Lay the towel (just 1 layer) inside a strainer and pour the puree in, then take up the corners of the towel and twist to make a sack with the puree inside. You should be able to squeeze the juice out slowly by twisting it tighter. Or if you have patience, you can leave it in the fridge overnight and see how much drips out.