Remove heads and tails from radishes; wash. Using bottom of heavy drinking glass, about 2" across base, hit radishes on side to crack them - not mash them - so dressing can get into flesh. Avoid rendering a crushing blow no matter how you feel that day. Sprinkle radishes all over with salt, put them in a bowl, and set aside for about 15 minutes at room temperature.
Prepare dressing: Combine vinegar, sugar, thin soy sauce, peanut oil, sesame oil and fresh ginger juice. Double amount of vinegar for a sharper taste, if desired. Drain liquid from radishes (salt will have drawn off quite a bit of water); pour dressing over them; cover and refrigerate for 30 minutes. If you make this dish ahead of time, pour on dressing 30 minutes before serving. Immediately before serving, transfer radishes to serving dish; garnish with Chinese parsley and serve.