Tenderize: Cover the chicken breasts with plastic wrap or gallon size resealable plastic bag and pound with a rolling pin or meat tenderizer until uniformly thick.
Season: Cover both sides of chicken breasts with lemon zest, pepper, and about half of the salt. Dredge them in flour and shake off any excess flour.
Cook: Heat the olive oil and 2 tablespoons of butter over medium high heat in a large skillet. Ideally the temperature of the oil will be 350°F prior to adding the chicken. Pan-fry the chicken breasts, taking care not to overcrowd the pan.
Turn: Cook until the bottom is dark golden brown, then flip them over, reduce heat to low, insert a thermometer into the thickest part of the meat, and cover. Cook until the internal temperature reaches 165 degrees F, then immediately transfer chicken to a plate and loosely tent with foil.
Make sauce: Using the pan you cooked the chicken in over low heat, add the remaining 4 tablespoons of butter, lemon juice, honey, parsley, and remaining salt. Scrape and dissolve any brown bits from the bottom of the skillet. Let cook for a few minutes until the butter melts and the sauce is fully mixed. Taste the sauce and if it's too tart, add small amounts of salt and/or honey and continue to taste until it's perfect.
Serve: Slice the chicken on a cutting board, then add the chicken as well as any juice from the plate back to the pan with the sauce and spoon sauce over chicken. Serve and enjoy!