Place each steak between two sheets of plastic wrap and pound with a meat mallet until about ½ inch thick; set aside.
On a shallow plate, combine the flour, salt, and pepper.
In a second shallow bowl, whisk the eggs until smooth.
In a third shallow bowl, mix the bread crumbs, Parmesan, and chopped parsley.
Working with one steak at a time, dredge it in the flour mixture and shake off excess, dip into the beaten eggs, then press both sides into the breadcrumb mixture until well coated.
Heat the oil in a large skillet over medium heat until shimmering. Add breaded steaks without crowding and cook 2–3 minutes per side, or until golden and crispy and cooked through.
Transfer cooked milanesa to a paper towel-lined plate to drain excess oil. Repeat with remaining steaks.