Put the licorice in the freezer to let it get rock hard.
Meanwhile, bring a large pot of water to a boil. Add the red wine vinegar and beets. Boil, covered, for 20 to 30 minutes, or until you can stick them with a fork and it comes out easily. When the beets are cooked, peel and chop them (while still warm) into bite-size pieces.
Whisk together the fruit vinegar, mustard, wasabi, and walnut oil. Toss the beets in the mixture and season to taste with salt and pepper. Fold in the orange, avocado, and basil.
Remove the licorice from the freezer and shave atop the salad as you would Parmesan cheese.