Trim about 1/4-inch from stem ends of Brussels sprouts. Remove any wilted outer leaves and discard. Wash Brussels sprouts and pat dry. Peel away the green outer leaves individually, leaving the hard center cores (save the cores for another use).
In a large bowl combine the lemon juice, olive oil, salt, and pepper, whisking to combine. Add Brussels sprouts leaves, avocado, apple, pumpkin seeds, and Parmesan cheese to the bowl and toss to combine.