01 - Pat chicken breasts dry with paper towels. Season both sides generously with salt and black pepper. Dredge each piece lightly in flour, shaking off any excess coating.
02 - Heat olive oil and butter in a large skillet over medium-high heat until butter foams. Place chicken in pan and cook for 4–5 minutes per side until golden brown and internal temperature reaches 165°F. Transfer to a plate and tent loosely with foil.
03 - Reduce heat to medium. Add minced garlic to the same skillet and sauté for 1 minute until fragrant, being careful not to burn.
04 - Pour in chicken broth while scraping up browned bits from the bottom of the skillet with a wooden spoon. Let simmer for 2 minutes to reduce slightly.
05 - Stir in heavy cream, lemon zest, and lemon juice. Bring to a gentle simmer, then gradually whisk in Parmesan cheese until fully melted. Continue cooking for 2–3 minutes until sauce thickens enough to coat the back of a spoon.
06 - Return chicken to the skillet, spooning sauce generously over each piece. Simmer for 3–4 minutes until chicken is heated through. Sprinkle with chopped parsley and red pepper flakes if desired. Serve immediately with additional Parmesan and parsley on top.