01 - Season chicken breasts evenly with salt and pepper. Dredge each piece lightly in flour, shaking off any excess to ensure an even, thin coating.
02 - Heat a large skillet over medium-high heat and add olive oil with 1 tablespoon of butter. Once the fat is shimmering, add the chicken breasts. Sear for 5 to 6 minutes per side until golden brown and cooked through to an internal temperature of 165°F. Transfer to a plate and tent loosely with foil to retain heat.
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, being careful not to let it brown.
04 - Stir in the lemon zest, lemon juice, and chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the pan. Allow the sauce to simmer for 3 to 4 minutes until it begins to reduce slightly.
05 - Return the chicken and any accumulated juices to the skillet. Spoon the sauce over each piece and simmer for 2 to 3 minutes so the chicken absorbs the flavors.
06 - Scatter the freshly chopped parsley over the chicken and serve immediately, spooning extra sauce from the skillet over each portion.