Place each chicken breast in between 2 sheets of plastic wrap then pound to tenderize.
Sprinkle them with half of the salt and pepper.
On a plate, place the 1/2 cup flour then dredge the chicken on both sides. Shake off the excess.
In a small bowl, whisk the softened butter and 2 teaspoons flour until creamy. Set aside.
Over medium heat, in a medium nonstick saucepan, heat 2 tablespoons of olive oil then brown both sides of the chicken, about 4 minutes each or until cooked through. Transfer the cooked chicken to a plate then cover to keep them warm.
Using the same saucepan, wipe off the excess oil and flour with paper towels. Pour the chicken broth and lemon juice until it boils then whisk in the butter and flour mixture as well as the remaining oil, salt, and pepper. Whisk until everything comes together. Adjust the taste. Add the capers. Put back the cooked chicken and coat them with the sauce. Sprinkle the parsley and the lemon zest then turn off the fire.