Combine panko, parsley, and salt on a dinner plate. Mix egg and milk together in a bowl.
Dip fillets into the milk mixture and shake off excess. Lightly dredge in panko mixture.
Heat oil in a large, nonstick skillet over medium heat. Add fillets and cook until golden brown on 1 side, about 4 minutes. Turn and cook until fillets are no longer translucent in the center and they easily flake with a fork, about 5 minutes more. Serve immediately.
