Mince the shallot and ginger. Scrape into a small bowl or jar. Add a pinch of sea salt, the mustard, and 2 tablespoons vinegar. Emulsify with a fork, and then slowly add the olive oil, continuing to whisk until nice and thick. I like this dressing better as it marinates a bit–that’s why I’ve listed it first.
Next, heat 1 cup of water over high heat. When boiling, add a big pinch of salt and 1/2 cup bulgar. Bring back to a boil, cover, and turn heat down to simmer for 10 minutes. Remove lid and fluff.
Use a peeler to slice the carrot into long ribbons. Slice the radicchio into thin strips.
Toss the bulgar, carrots, radicchio, and tat soi with the dressing. Zest one of the oranges, and toss it into the salad. Supreme the oranges, and just before serving, place them throughout the salad, drizzle with a bit more dressing and gently toss.