Place the chicken breasts between two pieces of plastic wrap and pound to an even thickness. Season the chicken on both sides with garlic salt and freshly ground black pepper.
Mix together 1/2 cup all-purpose flour and 1/4 cup panko bread crumbs. Dredge the chicken lightly on all sides.
Over medium- high in a large skillet heat a few drizzles of olive oil with 2 Tbsp butter. Brown the chicken cooking for approximately 2-3 minutes on each side or until cooked through and the juices run clear. If the chicken is thicker, cook longer if thinner, cook for slightly less time. Add additional oil if needed when turning the chicken. Remove to a platter and keep warm.
Mix the remaining 2 Tbsp butter with 2 Tbsp all-purpose flour to form a paste.
Over medium-high heat add the chicken broth, white wine, lemon juice and zest to the same pan scraping the brown bits from the bottom of the pan.
Whisk in the butter-flour paste and cook until the sauce begins to thicken. Lower the heat and simmer for around 2-3 minutes to cook the flour and allow the lemon juice and wine to mellow. Taste and adjust the seasonings adding more garlic salt and black pepper to your taste. If you like the sauce thinner, add additional chicken broth at this point.
Add the capers and chopped parsley.
Serve the sauce drizzled over the chicken pieces. Garnish with lemon slices and additional parsley, if desired.
If desired, you may omit the wine and use all chicken broth instead. In that case, add 2 Tbsp white wine vinegar to the sauce.