Step 1: In a shallow bowl, mix the flour, salt, and pepper. Dredge each chicken breast in the mixture until coated, shaking off any excess.
Step 2: Heat olive oil and 2 tablespoons of butter in a large skillet over medium-high heat. Add the chicken and cook for 5-6 minutes per side until golden brown. Remove chicken from the pan and set aside.
Step 3: In the same skillet, add the minced garlic and cook for 1 minute until fragrant. Pour in the chicken broth and lemon juice, scraping the bottom of the pan to release the browned bits.
Step 4: Stir in the lemon zest and let the sauce simmer for 3-5 minutes until reduced by half. Whisk in the remaining 2 tablespoons of butter until the sauce is glossy.
Step 5: Return the chicken to the skillet and simmer for 2 minutes, spooning the sauce over the meat. Garnish with fresh parsley and serve immediately.