Make the dressing: In a blender or food processor, combine the Dijon mustard, mayonnaise, avocado oil, Parmesan cheese, lemon juice, garlic, and sardines (if using). Blend until smooth and creamy. Season with salt and pepper to taste.
On a cutting board, trim and thinly slice the Brussels sprouts. Chop.
On a cutting board, chop the arugula.
Assemble the salad: In a large bowl, combine the arugula, Brussels sprouts, sardines, and green olives.
Drizzle with the Caesar dressing and toss to coat. Serve immediately, topped with extra Parmesan cheese.