Slice pork tenderloin into 12 rounds. Place rounds between two sheets of plastic wrap; with a meat mallet or small heavy skillet, pound to 1/8 inch thick.
In a shallow bowl, beat egg whites with 1 tablespoon water. In another bowl, combine breadcrumbs and Parmesan. Place all-purpose flour in a third bowl. Season pork with salt. Dip pork in flour, then in egg mixture. Dredge in breadcrumb mixture; pat it in.
In a large nonstick skillet, heat olive oil over medium-high heat. Saute half the cutlets until golden brown and cooked through, about 1 minute per side. Repeat with another tablespoon oil and remaining pork. Serve with lemon wedges and parsley sprigs.