To make dressing: In food processor, process lemon juice, apple cider vinegar, pitted dates and mustard. Slowly add olive oil to combine.
To make salad: In large salad bowl, combine avocados, shaved Brussels sprouts, kale, red onion and pistachios. Drizzle salad dressing evenly over greens and toss until well-coated.
Serve with shaved Parmesan cheese, if desired.