1. Soak onion slices in small bowl of cold water for 15 to 20 minutes while preparing the rest of ingredients and then drain.
2. In small bowl, whisk together lemon juice, honey, mustard and a pinch of salt and pepper. Whisk in olive oil until dressing is emulsified. Set aside.
3. Trim Brussels sprouts. Using a mandoline, shave sprouts one at a time. Gentely separate the leaves so the shredded sprouts resemble a fine slaw.
4. Put sprouts into serving bowl and gently toss with onions and dressing. Fold in pecorino and adjust seasonings to taste.