For the arugula and vinaigrette: Whisk together the mustard, vinegar, shallots, oregano and garlic in a large bowl. Drizzle in the olive oil and whisk to combine. Set aside.
For the pork: Put the panko, Parmigiano-Reggiano, oregano and cookies in a food processor and pulse until finely ground. Transfer to a shallow dish. Put the eggs and flour in separate shallow dishes.
Season the pork on both sides with salt and pepper. In order, dip one of the cutlets first in the flour, then in the egg and finally in the cookie mixture, being sure to shake off any excess after each step. Repeat with the other cutlet.
Heat the butter, thyme and sage in a large saute pan over medium-high heat. When hot, add the cutlets and lower the heat to medium low. Slowly brown the cutlets on one side, about 3 minutes. Flip and repeat on the other side. Drain on a rack and immediately season with salt and pepper.
Toss the arugula in the vinaigrette and season with salt and pepper. Divide the pork cutlets and salad between plates.