Prepare the Brussels Sprouts by giving them a good rinse and patting them dry. Trim off the tough bottom end and remove any bruised or yellowed outer leaves. Using a mandoline slicer, shave the Brussels sprouts as thinly as possible, or cut with a sharp knife as thinly as possible. Place all the shaved sprouts into a large bowl.

In a small dry skillet over medium heat, toast the pecans for 3 to 5 minutes until fragrant and lightly browned. Immediately remove and set aside to cool.

Whisk together the olive oil, lemon juice, Dijon mustard, honey or maple syrup, minced garlic, and salt and pepper until the dressing emulsifies and becomes creamy.

Pour about two thirds of the vinaigrette over the shaved Brussels sprouts. Gently massage the dressing into the sprouts for about 30 seconds. Let them sit and marinate for at least 15 to 20 minutes.

Just before serving, add the toasted pecans, pomegranate seeds, and grated Pecorino cheese to the bowl with the dressed sprouts. Add the remaining dressing if needed. Gently toss to combine. Transfer to a serving platter and enjoy.