Combine flour, lemon zest, parmesan cheese, salt and pepper in a shallow dish. Butterfly chicken breasts by slicing them in half to create two thin chicken pieces. If chicken breasts are still uneven, pound with a meat mallet. Dredge chicken in flour mixture, shaking off excess.
Heat oil and butter in a saucepan over medium high heat. Once hot, sear chicken for 4 minutes on each side or until golden and fully cooked. Remove from pan.
Reduce heat to medium. Add butter and garlic, then cook until garlic is fragrant. Add flour and stir to create a roux, then cook for 1 minute.
Slowly whisk in chicken broth, then white wine, lemon juice, and capers. Cook for 5-10 minutes or until thickened.
Stir in parsley, then add chicken back to the pan to reheat and be coated. Serve immediately.
Notes
For wine, a dry pinot grigio or sauvignon blanc works best. Serve over pasta, rice, or mashed potatoes.