Place pork cutlets between two sheets of parchment paper; using a meat mallet or a small, heavy skillet, pound to 1/8 inch thick. Season both sides of pork with salt and pepper.
Heat 2 tablespoons oil in a large saucepan over medium-high heat. Working in two batches, add pork to pan, and cook, flipping once, until golden brown, 1 1/2 to 2 minutes per side. (If pan becomes dry, add more oil.) Transfer to a platter.
Drizzle lemon juice over pork, and sprinkle with grated Parmesan. Garnish with Parmesan curls and parsley. Serve with lemon wedges and mustard.