Trim the tough stem ends off brussels sprouts and discard loose outer leaves. Using a mandoline slicer, food processor with slicing disc, or sharp chef's knife, shave sprouts paper-thin. Place in a large salad bowl.

Heat a small dry skillet over medium-low heat. Add walnut halves and toast for 4 to 5 minutes, swirling pan frequently until fragrant and lightly golden. Remove from heat, cool for 2 minutes, and roughly chop.

In a mason jar or small bowl, combine extra virgin olive oil, fresh lemon juice, whole grain Dijon mustard, honey, minced garlic, sea salt, and black pepper. Seal and shake vigorously (or whisk) until completely emulsified and creamy.

Pour half of the vinaigrette over the shaved brussels sprouts. Use salad tongs or clean hands to gently massage the dressing into the greens for 60 seconds. Let sit at room temperature for 10 minutes to allow the acid to tenderize the leaves.

Add the toasted walnuts, pomegranate arils, and shaved Pecorino Romano to the bowl. Drizzle with the remaining dressing and toss gently to combine.

Transfer to a shallow serving platter or wide ceramic bowl. Garnish with a few extra cheese curls and freshly cracked black pepper. Serve immediately.