01 - Pat chicken breasts dry with paper towels. Season both sides generously with salt and black pepper. Lightly dredge each piece in flour, shaking off excess coating.
02 - Heat olive oil and butter in a large skillet over medium-high heat until shimmering. Add chicken breasts and sear for 4-5 minutes per side until golden brown and cooked through. Transfer to a plate and tent loosely with foil to rest.
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, using a wooden spoon to scrape up any browned bits from the bottom of the pan. 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 and sauce has thickened, about 2-3 minutes.
06 - Return chicken and any accumulated juices to the skillet. Spoon sauce generously over each piece. Simmer for 3-4 minutes until chicken is heated through.
07 - Sprinkle with chopped fresh parsley and red pepper flakes if using. Serve immediately with additional Parmesan and parsley on the side.