Slice each chicken breast in half lengthwise to make thinner cutlets; pat dry.
Season both sides of the cutlets with salt, pepper, and garlic powder.
Lightly dredge each cutlet in flour, shaking off excess.
Heat the olive oil and 1 tablespoon butter in a large skillet over medium-high heat until shimmering.
Add the chicken cutlets to the hot skillet and cook for 4–5 minutes per side, until golden brown and cooked through; transfer to a plate.
Reduce heat to medium and add the chicken broth, lemon juice, lemon zest, and the remaining 2 tablespoons butter to the skillet; simmer for 2–3 minutes to reduce slightly.
Return the chicken to the pan and spoon the sauce over it; cook 1–2 more minutes until heated through and the sauce coats the chicken.
Taste and adjust seasoning with salt and pepper, then sprinkle with chopped parsley if using and serve.