Pound and season the chicken: If using breasts, pound to an even 1/2-inch thickness for quick, even cooking. Pat dry. Season both sides with salt and pepper, then lightly dredge in flour, shaking off excess.
Sear the chicken: Heat olive oil in a large skillet over medium-high.
Add the chicken and cook 4–5 minutes per side until golden and cooked through (165°F). Transfer to a plate and tent with foil.
Build the flavor base: Reduce heat to medium. Add butter to the pan.
Stir in minced garlic and cook 30–45 seconds until fragrant. Do not brown the garlic.
Deglaze: Pour in the chicken broth. Scrape up the browned bits from the pan with a wooden spoon.
Simmer 2–3 minutes to reduce slightly.
Add lemon and cream: Stir in lemon zest, lemon juice, and heavy cream. Bring to a gentle simmer. If using Parmesan, whisk it in now.
Season with salt, pepper, and red pepper flakes, to taste.
Thicken and finish: Simmer 2–4 minutes until the sauce lightly thickens and coats a spoon. If it’s too thick, add a splash of broth. If too thin, simmer a bit longer.
Return the chicken: Nestle the chicken back into the pan, along with any juices from the plate.
Spoon sauce over the top and warm through for 1–2 minutes.
Garnish and serve: Sprinkle with fresh herbs. Taste and adjust lemon or salt if needed. Serve hot with mashed potatoes, rice, pasta, or crusty bread to catch the sauce.