In a medium bowl, combine the egg and half & half and beat together well. In a separate medium bowl, combine the Bread crumbs, cheese, basil Rinse chicken and pat dry. Dip each piece into the egg wash and then dredge liberally in the cracker crumb mixture. Heat the olive oil in a large skillet over medium high heat. Fry the chicken in the oil for 5 minutes per side, or until both sides are golden brown and crusty. Place chicken in a 9x13 baking dish. Bake, covered, at 400 degrees F for 15 minutes, or until chicken juices run clear.
Meanwhile in pan add 2 tablespoons butter and 1/3 cup chicken broth. carefully sprinkle in wondra flour to thicken.