First, make the dressing. In a small bowl or jar, whisk together the olive oil, apple cider vinegar, lemon juice, maple syrup, Dijon mustard, and minced garlic. Season with salt and pepper and set aside.
Using a food processor slicing attachment, shave the Brussels sprouts to thinly slice. Place in a large bowl.
Add pomegranate arils, chopped apple, sliced almonds, sunflower seeds, dried cranberries and Parmesan cheese.
Drizzle the dressing over the salad and toss well to evenly coat.