If breasts are thick, butterfly each or pound to an even 1/2-inch thickness between two sheets of plastic wrap using a meat mallet or rolling pin. Season both sides with 1 tsp kosher salt and 1/2 tsp black pepper.

Set up dredging stations

Place the flour in a shallow dish and season with remaining 1/2 tsp salt and a pinch of pepper. Beat the eggs in a second shallow dish. In a third dish combine panko and grated Parmesan.

Coat the chicken

Working with one breast at a time: dredge in flour, shaking off excess; dip into beaten eggs, letting excess drip off; press into panko-Parmesan mixture until well coated on both sides. Set on a plate and repeat.

Pan-fry

Heat a large skillet over medium heat. Add olive oil and butter and let butter melt and foam. When the fat is shimmering (about 1–2 minutes), add chicken and cook 3–4 minutes per side until golden brown and internal temperature reaches 165°F (74°C). Adjust heat as needed to avoid burning; add a little more oil if pan looks dry.

Transfer cooked chicken to a paper-towel-lined plate to rest for 5 minutes before serving to let juices redistribute.

Optional garnish & serving

Serve each chicken breast with a lemon wedge and sprinkle with chopped parsley. Taste and add extra salt and pepper if desired.