1. Soak the onion slices in a small bowl of cold water for 15 to 20 minutes while preparing the rest of the ingredients and then drain.
2. 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.
3. Trim all of the Brussels sprouts. Using a mandoline, shave the sprouts one at a time. Gentely separate the leaves so the shredded sprouts resemble a fine slaw.
4. Put the sprouts ina serving bowl and gently toss with the onions and the dressing. Fold in the pecorino and adjust the seasonings to taste.