Heat a large skillet to medium-high.
Pound chicken to a flat even thickness about ½-inch thick. Sprinkle both sides of the chicken breasts with Italian seasoning and ground black pepper.
Add 1 tablespoon of the reserved oil of the pesto to your skillet. Swirl the oil around to cover the bottom. Sear the chicken for 4 to 5 minutes on each side until golden. Remove the chicken from the pan and set it aside.
Add the white wine or chicken broth, pesto, heavy cream, and feta to the pan. Whisk well.
Add the chicken back into the pesto cream sauce and cover. Cook for about 5 minutes to allow the cheese to melt and the sauce to thicken.
Top the chicken with shaved parmesan cheese for garnish (optional) and serve.
