Soak the onion slices in a small bowl of cold water for 15 to 20 minutes while you prepare the rest of the ingredients.
In a small bowl, whisk together the lemon juice, honey, mustard and a pinch of salt and pepper. Whisk in the olive oil until the dressing is emulsified. Set aside.
Trim all of the Brussels sprouts, cutting off any bruised outer leaves and slicing off a good portion of the hard root end. Using a mandoline, shave the sprouts one at a time. When you''re done, use your fingers to gently separate the leaves so that the shredded sprouts resemble a very fine slaw.
Put the sprouts in a serving bowl and toss gently with the onions (which you''ve now drained) and the dressing. Fold in the pecorino, taste and adjust seasonings if necessary. Serve immediately, before it starts to wilt!
