Step 1: In a shallow bowl, whisk together the flour, salt, and pepper. Dredge each chicken breast in the flour mixture, shaking off any excess.
Step 2: Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the chicken and cook for 5-6 minutes per side, or until golden brown and cooked through. Remove chicken from the pan and set aside.
Step 3: Reduce heat to medium. Add the minced garlic to the same skillet and sauté for 1 minute until fragrant. Do not let it burn.
Step 4: Pour in the chicken broth, lemon juice, and lemon zest. Use a wooden spoon to scrape up the browned bits from the bottom of the pan. Let the sauce simmer for 3-5 minutes until it reduces slightly.
Step 5: Stir in the remaining 2 tablespoons of butter until melted and the sauce is glossy. Return the chicken to the pan, spooning the sauce over it. Garnish with parsley and serve immediately.