Preheat the broiler.
Toss the artichokes with 1 tablespoon of oil, 1/4 teaspoon salt and pepper to taste. Broil until browned on all sides, stirring occasionally, 5 to 7 minutes. Set aside.
Toss the arugula with the fennel and artichokes in a large bowl. Whisk together the vinegar, mustard, the remaining 1 tablespoon oil, 2 teaspoons water, 1/4 teaspoon salt and pepper to taste in a small bowl. Pour over the salad and toss well to coat. Season with additional salt and pepper. Top with the Parmesan.