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 excess coating.
02 - Heat olive oil and butter in a large skillet over medium-high heat until butter foams. Add chicken breasts and sear for 4 to 5 minutes per side until golden brown and cooked through. Transfer to a plate and tent loosely with aluminum 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, using a wooden spoon to scrape up any browned bits from the bottom of the skillet. 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 thickens, about 2 to 3 minutes.
06 - Return chicken to the skillet, spooning sauce generously over each piece. Simmer for 3 to 4 minutes until heated through. Sprinkle with chopped parsley and red pepper flakes. Serve immediately with additional Parmesan and parsley.