Combine the garlic, ginger, mustard, and apple cider vinegar. Slowly whisk in the olive oil, then season to taste with salt. Set aside.
In a small saucepan, bring 1 cup of water to a boil over high heat. Stir int he bulgur and a pich of salt. Return to a boil, then reduce heat to low and cover. Cook, undisturbed, for 10 minutes, then remove the lid and fluff with a fork. Place in a large serving bowl.
Slice the carrots into long thin ribbons with a vegetable peeler. Thinly slice the radicchio. Zest one of the oranges, then slice the oranges into segments. Add the carrots, radicchio, orange zest, and orange segments to the bowl of bulgur, and toss well to combine. Fold in the torn spinach or tatsoi and then drizzle with some dressing. Taste and adjust seasoning if needed, and serve with more dressing at the table.