01 - Season chicken breasts generously with salt and pepper. Dredge each piece lightly in flour, shaking off any excess.
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. Transfer to a plate and tent loosely with foil.
03 - Reduce heat to medium. Add the remaining 2 tablespoons of butter to the skillet and swirl until melted. Sauté minced garlic for about 1 minute until fragrant, taking care not to brown.
04 - Stir in lemon zest, lemon juice, and chicken broth, scraping up any browned bits from the bottom of the skillet. Let the sauce simmer for 3 to 4 minutes until slightly reduced.
05 - Return the chicken along with any accumulated juices to the skillet. Spoon the sauce over each piece and simmer for an additional 2 to 3 minutes to meld the flavors.
06 - Scatter freshly chopped parsley over the chicken and serve immediately, spooning extra sauce over each portion.