Make sure the chicken breasts are no more than 3/4” thick. Cut them in half if necessary. Using a large cast-iron saucepan or one with a metal handle, heat the oil and butter over medium-high heat on the stovetop. Dredge each chicken breast in flour, and brown them on both sides.
Once browned, take the pan off the heat and pour the soup over top. (If you do not have a pan that can go in the oven, transfer the browned chicken to a casserole dish first.) Arrange the mozzarella and whole basil leaves on top. Bake uncovered for about 30 minutes, or until the internal temperature of the chicken reaches at least 170 degrees.