Separate the tenderloins from the breasts. Between sheets of plastic wrap pound the thicker side of the breast to make it more even in thickness. Season the chicken with salt. Heat the olive oil in a large skillet over moderate heat. Add the chicken breasts and tenderloins. Saute for about 4 to 5 minutes. You'll know to turn the chicken over when the top looks opaque (tenderloins may take only 2 to 3 minutes per side). Saute on other side 4 to 5 minutes or until the interior is cooked through. Mix lemon zest and lemon juice into chicken broth.
Remove the chicken to a plate. Give the lemon broth cornstarch mixture a stir and add it to skillet. Deglaze the pan and simmer for a two minutes or until the sauce looks thick and glossy. Taste and season with salt and pepper. Remove the skillet from the heat and whisk in the butter if you wish. Pour the sauce pour over the chicken and sprinkle the scallions on top.