Prepare the vinaigrette. In a small bowl, whisk together the lemon juice, olive oil, and dijon mustard. Season to taste with salt and pepper.
Place the arugula in a large mixing bowl. With a vegetable peeler or sharp knife, shave some parmesan into strips and toss together with the arugula. Add parmesan until you have enough to your liking mixed throughout the arugula. Slowly start to drizzle some of the dressing into the bowl, tossing the arugula and parmesan until it is all lightly coated. Do not overdress the salad (you will have dressing leftover). Taste. Season with sea salt and black pepper. Serve immediately.