Remove any bruised outer leaves from the brussels sprouts. Holding each brussels sprout by the stem end, cut into very thin slices. Toss in a bowl to separate layers. Add half the pomegranate arils to the brussels sprouts and toss.
For the poppy seed dressing, combine all ingredients in a mason jar shake until well combined. Season to taste with salt and pepper. Start by adding half the poppy seed dressing. Toss the salad to coat. Continue to drizzle on the dressing until it is dressed to your liking.
Arrange the salad on a platter and top the salad with the remaining pomegranate arils.