Trim the stem ends from the Brussels sprouts and cut each one in half lengthwise. Shave crosswise as thinly as you can with a sharp knife, or use a food processor fitted with the slicing blade; you should have about 8 cups.
Whisk the olive oil, lemon juice, Dijon mustard, honey, salt and pepper in a large bowl until smooth.
Add the shaved sprouts and toss to coat, then massage the dressing into the sprouts with clean hands for 1 minute, until they begin to soften.
Fold in the dried cranberries and toasted pecans and let the salad sit for 10 minutes so the sprouts absorb the dressing.
Taste and adjust the salt and lemon juice, transfer to a serving bowl and top with the shaved Parmesan just before serving.
