In a small skillet over medium heat, toast the nuts until fragrant, about 5 minutes, tossing often.
Transfer to a plate to cool off; set aside.
Using a food processor with the slicing disc on, process the prepared sprouts; set aside.
Pour lemon juice on the apple cubes and toss to coat.
To assemble... In a large salad bowl, add shaved Brussels sprouts, onions, pomegranate seeds, apple cubes, toasted walnuts and cheese. Toss until the ingredients are well mixed and serve immediately.