Prepare the vinaigrette by whisking together olive oil, lemon juice, Dijon mustard, honey, salt, and pepper in a small bowl until fully emulsified.

Use a mandoline or food processor with a slicing blade to finely shave the trimmed Brussels sprouts into a large mixing bowl.

Add the julienned apples and pomegranate arils to the bowl with the sprouts.

Drizzle the vinaigrette over the vegetables and toss thoroughly to ensure even distribution and light maceration of the sprouts.

Fold in half of the shaved Manchego cheese and the toasted walnuts.

Transfer to a serving platter and garnish with the remaining Manchego cheese.

Allow the salad to rest at room temperature for 10 minutes prior to service to soften the fibrous texture of the raw sprouts.