01 - Season chicken breasts generously with salt and pepper. Dredge each piece lightly in flour, shaking off any excess to ensure an even, thin coating.
02 - Heat olive oil and 1 tablespoon of 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 deeply golden and cooked through. Transfer to a plate and tent loosely with foil to rest.
03 - Reduce the heat to medium. Add the remaining 2 tablespoons of butter to the skillet and let it melt. Add the minced garlic and sauté for about 1 minute until fragrant and just beginning to color, taking care not to burn.
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 and thicken 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 until the chicken is warmed through and well coated.
06 - Scatter freshly chopped parsley over the chicken and serve immediately, spooning extra sauce from the pan over each portion.