Prep the chicken. Pound thicker ends to an even thickness for even cooking. Pat dry. Season both sides with salt and pepper. If using, lightly dredge in flour and shake off excess.

Sear to golden. Heat olive oil and 1 tablespoon butter in a large skillet over medium-high. When shimmering, add chicken in a single layer. Cook 4–6 minutes per side until deeply golden and just cooked through. Transfer to a plate and tent with foil.

Build the flavor base. Lower heat to medium. Add remaining 1 tablespoon butter, then the garlic. Cook 30–45 seconds until fragrant. Don’t let it brown.

Deglaze with broth. Stir in chicken broth, scraping up browned bits. Simmer 2–3 minutes to reduce slightly. Those bits are pure flavor.

Add cream and seasonings. Pour in heavy cream. Stir in lemon zest, Italian seasoning, and a pinch of red pepper flakes if using. Simmer gently 2 minutes.

Finish with lemon and Parmesan. Add 2 tablespoons lemon juice and Parmesan. Stir until smooth. Taste, then add more lemon juice to reach a bright, balanced tang. The sauce should be glossy and lightly thickened.

Return the chicken. Nestle chicken (and juices) into the sauce. Add capers if using. Simmer 2–3 minutes to warm through and let flavors marry.

Adjust and garnish. Taste for salt, pepper, and lemon. If sauce is too thick, loosen with a splash of broth. If too thin, simmer 1–2 minutes more. Finish with chopped parsley and lemon slices.

Serve right away. Spoon sauce over chicken and pair with rice, mashed potatoes, pasta, or crusty bread. Steamed greens or a simple salad keep things fresh.