Prep the chicken: Slice chicken breasts in half horizontally to make thinner cutlets, or use thighs as is. Pat dry. Season generously with salt and pepper.
If using flour, lightly dredge both sides, shaking off excess.
Heat the skillet: Set a large skillet over medium-high heat. Add olive oil and 1 tablespoon butter. When the butter foams, add the chicken in a single layer without crowding.
Brown the chicken: Cook 4–5 minutes per side until golden and cooked through (internal temp 165°F).
Transfer to a plate and tent loosely with foil.
Build flavor: Reduce heat to medium. Add 2 tablespoons butter to the skillet. Stir in garlic and cook 30–60 seconds until fragrant.
Don’t let it burn.
Deglaze: Pour in chicken broth and scrape up browned bits with a wooden spoon. Stir in lemon juice, herbs, and red pepper flakes. Simmer 2–3 minutes until slightly reduced.
Finish the sauce: Stir in remaining 1 tablespoon butter for a glossy finish.
Taste and adjust salt, pepper, and lemon.
Return the chicken: Add chicken and any juices back to the skillet. Spoon sauce over the top and simmer 1–2 minutes to warm through.
Garnish and serve: Sprinkle with parsley and Parmesan if using. Serve immediately with your favorite sides.