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 the heat to medium and add the remaining 2 tablespoons butter to the skillet. Cook the minced garlic for about 1 minute until fragrant, being careful not to let it brown.
04 - Stir in the 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 until it begins to reduce slightly.
05 - Return the chicken along with any accumulated juices to the skillet. Spoon the sauce over each piece and simmer for 2 to 3 minutes to let the flavors meld.
06 - Scatter fresh chopped parsley over the chicken and serve immediately, spooning extra sauce from the pan over each portion.