01 - Pat chicken breasts completely dry with paper towels. Season both sides generously with salt and black pepper. Dredge each breast lightly in flour, coating evenly and shaking off any excess.
02 - Heat olive oil and butter in a large skillet over medium-high heat until butter foams. Add chicken breasts and sear for 4–5 minutes per side until golden brown and cooked through to an internal temperature of 165°F. Transfer to a plate and cover 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 it.
04 - Pour in chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the skillet. Let the broth simmer and reduce for 2 minutes.
05 - Stir in heavy cream, lemon zest, and lemon juice. Bring to a gentle simmer, then gradually whisk in grated Parmesan cheese until completely melted and sauce thickens slightly, about 2–3 minutes.
06 - Return chicken breasts to the skillet, spooning sauce generously over each piece. Simmer for 3–4 minutes until chicken is heated through. Sprinkle with chopped parsley and crushed red pepper flakes. Serve immediately with additional Parmesan and parsley for garnish.