01 - Season chicken breasts evenly with salt and pepper. Dredge each piece lightly in flour, shaking off any excess coating.
02 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Once the fat is shimmering, add the chicken breasts and cook for 5 to 6 minutes per side until golden brown and cooked through. Transfer to a plate and tent loosely with foil to rest.
03 - Reduce heat to medium. Add the remaining 2 tablespoons butter to the skillet and let it melt. Sauté minced garlic for about 1 minute until fragrant but not browned.
04 - Stir in lemon zest, lemon juice, and chicken broth, scraping up any browned bits from the bottom of the pan. Let the sauce simmer for 3 to 4 minutes to reduce slightly.
05 - Return the chicken and any accumulated juices to the skillet. Spoon the sauce over each piece and simmer for an additional 2 to 3 minutes to meld flavors.
06 - Scatter freshly chopped parsley over the chicken and serve immediately, spooning extra sauce over each portion.