Cover the chicken breasts with plastic wrap and pound with a rolling pin or meat tenderizer until uniformly thick. Season the chicken breast pieces with salt and pepper and dredge them in flour. Shake off excess flour.
Heat the olive oil and 2 tablespoons of butter over medium high heat in a large skillet. Pan-fry the chicken pieces until golden brown on both sides, about 3 minutes per side. Work in batches if necessary so as to not over crowd skillet (more oil and butter can be added as needed, however it must be heated before adding additional chicken). The goal is to give the chicken a nice golden brown on each side but not cook it all the way through. It will finish cooking in the sauce at the end. Place the chicken pieces onto a plate and tent with foil.
Using the pan you cooked the chicken in, cook and stir the minced garlic in the skillet until fragrant, about 20 seconds. Pour in the chicken broth and white wine as well as the lemon zest. Scrape and dissolve any brown bits from the bottom of the skillet. Let cook, stirring occasionally, until the sauce reduces by about half, 5 to 8 minutes.
Add the lemon juice and capers. Simmer until the sauce is reduced and slightly thickened, about 5 minutes more. Drop the remaining butter and honey into the skillet and swirl it into the sauce by tilting the skillet until the butter is melted and incorporated.
Add the chicken as well as any juice from the plate back to the pan with the sauce and spoon sauce over chicken. Continue cooking over low heat or transfer to 200 degree F oven to finish cooking, about 5-10 minutes.
Add the parsley, stir, and remove from heat and serve.