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 butter foams. Add chicken breasts and sear 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 skillet and cook 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 whisk in 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 heated through. Garnish with chopped parsley and red pepper flakes if desired.