Prep the chicken: Butterfly large breasts into cutlets or pound to an even 1/2-inch thickness.
Pat dry. Season both sides with salt and pepper.
Lightly coat: Add the flour to a shallow dish. Dredge each cutlet, shaking off excess.
You want a whisper-thin coating, not a crust.
Sear the chicken: Heat a large skillet over medium-high. Add olive oil and 1/2 tablespoon butter. When shimmering, cook chicken in batches 2–3 minutes per side until golden and just cooked through.
Transfer to a plate and tent with foil.
Sauté aromatics: Reduce heat to medium. Add remaining 1/2 tablespoon butter. Sauté garlic (and shallot, if using) for 30–60 seconds, just until fragrant.
Don’t brown the garlic.
Deglaze: Pour in the chicken broth, scraping up browned bits. Simmer 2 minutes to reduce slightly.
Add lemon and capers: Stir in lemon juice, lemon zest, and capers. Simmer 2–3 minutes more.
Taste and adjust with a pinch of salt if needed.
Optional protein boost: For Greek yogurt: whisk 2–3 tablespoons of warm sauce into the yogurt to temper, then stir that back into the pan off the heat for a creamy finish. For whey isolate: whisk 1 scoop with 2–3 tablespoons cool broth until smooth, then whisk into the sauce off heat. Do not boil after adding either; gentle heat keeps it smooth.
Return chicken to the pan: Nestle cutlets into the sauce with any accumulated juices. Warm 1–2 minutes, spooning sauce over the top.
Finish and serve: Sprinkle with parsley.
Garnish with lemon slices. Serve over cauliflower mash, zucchini noodles, steamed greens, or whole-grain pasta, and spoon plenty of sauce on top.