Prep the chicken: Pat dry and season both sides with salt and pepper. If breasts are thick, slice them horizontally to create thinner cutlets for even cooking.
Sear for color: Heat olive oil and 1 tablespoon butter in a large skillet over medium-high.
Add chicken in a single layer. Sear 3–5 minutes per side until golden and just cooked through. Transfer to a plate and tent loosely with foil.
Build the flavor base: Reduce heat to medium.
Add remaining 3 tablespoons butter. Stir in garlic and cook 30–60 seconds until fragrant, not browned.
Deglaze: Pour in chicken broth and lemon juice. Scrape up brown bits.
Simmer 2–3 minutes to reduce slightly.
Brighten and balance: Stir in lemon zest, red pepper flakes, and capers if using. Taste and adjust salt and pepper. If you want a silkier finish, whisk in Parmesan off heat.
Return the chicken: Add chicken and any juices back to the pan.
Spoon sauce over the top and simmer 1–2 minutes to warm through.
Finish: Sprinkle with parsley. Serve with sautéed greens, roasted broccoli, or cauliflower mash to keep it low carb.