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 large skillet over medium-high heat. Add chicken breasts and sear 4 to 5 minutes per side until golden brown and cooked through. Transfer to plate, cover loosely with foil.
03 - Reduce heat to medium. Add minced garlic to skillet and cook 1 minute until fragrant, being careful not to burn.
04 - Pour in chicken broth, using wooden spoon to scrape up browned bits from bottom of skillet. Let simmer 2 minutes to reduce slightly.
05 - Stir in heavy cream, lemon zest, and lemon juice. Bring to gentle simmer. Whisk in Parmesan cheese until fully melted and sauce thickens slightly, 2 to 3 minutes.
06 - Return chicken to skillet, spooning sauce generously over each piece. Simmer 3 to 4 minutes until chicken is heated through. Sprinkle with fresh parsley and red pepper flakes if desired.