Toast the walnuts in a toaster oven or by tossing them in a dry skillet over medium heat.
Place the arugula in a large bowl and toss with the vinaigrette dressing. Divide the arugula among 4 plates.
Top each portion with some shaved Parmesan and a scattering of walnuts.
Garnish each plate, if desired, with 3 to 4 sweet and sour shallots.