Prep the chicken. If using whole breasts, slice them in half horizontally to make thin cutlets. Pat dry. Season both sides with salt and pepper.

Set up your dredging station. Place flour on a plate. In a shallow bowl, beat the eggs and stir in lemon zest and Parmesan (if using). Keep it close to the stove.

Coat the chicken. Dredge each cutlet lightly in flour, shaking off extra. Dip into the egg mixture, letting excess drip off. You want a thin, even coating.

Heat the pan. In a large skillet over medium heat, add 1 tablespoon butter and the olive oil. When hot and shimmering, add the cutlets in a single layer.

Sear until golden. Cook chicken 3–4 minutes per side until nicely browned and just cooked through. Work in batches if needed. Transfer to a plate and tent with foil.

Sauté the garlic. Reduce heat slightly. Add the minced garlic to the pan and cook 20–30 seconds, just until fragrant. Do not let it brown.

Deglaze with wine. Pour in the white wine. Scrape up any browned bits with a wooden spoon. Simmer 1–2 minutes to reduce slightly.

Add lemon and broth. Stir in the lemon juice and chicken broth. Simmer 2–3 minutes to let the flavors meld. Taste and season with salt and pepper.

Finish the sauce. Whisk in 1 tablespoon butter to round out the sauce. For a slightly thicker sauce, whisk 1 teaspoon flour with 1 tablespoon water, then whisk that slurry into the pan. Simmer 1 minute.

Return the chicken. Add the cutlets and any juices back to the pan. Spoon sauce over the top and simmer 1 minute to coat and rewarm.

Garnish and serve. Remove from heat. Stir in chopped parsley and garnish with lemon slices. Serve immediately with extra sauce spooned over.