Combine first 4 ingredients in a shallow dish. Set aside.
Place flour in a shallow dish. Whisk eggs in a medium bowl. Sprinkle fish with salt and pepper, and dredge in flour. Shake off excess, dip fish into egg, and press gently into breadcrumb mixture.
Heat 2 tablespoons butter and 2 tablespoons oil in a large heavy skillet over medium heat until butter melts. Add 2 fish fillets; cook 3 minutes on each side or until golden. Repeat with remaining butter, oil, and fish. Garnish, if desired.