To prepare dressing, whisk together cider vinegar and honey. Drizzle in olive oil and whisk until combined. Season to taste with salt and pepper.
Core apple and cut into small cubes or matchsticks. Place in a small bowl and toss with 1 tablespoon of dressing to prevent the apples from browning.
Trim ends of Brussels sprouts and remove any outer damaged leaves and discard. Using a mandoline slicer or a very sharp knife, slice sprouts as thinly as possible (about 1/16 of an inch). Discard ends and any large core pieces or chunks.
Place shaved sprouts in a large bowl. Toss with apples and remaining dressing. Set aside and let sit for at least 15 minutes or more.
Divide salad among serving dishes, and top with a healthy sprinkling of grated Pecorino.
