Cut each chicken breast in half with a sharp chef’s knife, making two slices out of each breast (or have butcher do it). Season chicken all over with 1/2 teaspoon salt.
Spread flour on a rimmed plate, then dredge chicken in flour and tap off excess
Melt the butter and the oil in a large skillet over medium heat. When the butter is melted, add the chicken and cook until browned on one side, about 2 minutes. Flip the pieces, and brown the other side, about 2 minutes more.
When the chicken is browned, pour the tomatoes, roasted peppers, oregano, and remaining 1 teaspoon salt into skillet. Bring to a simmer, and cook until the ingredients come together as a sauce, about 5 minutes.
Sprinkle the chicken with the cheese and shredded basil, Cover the skillet, and simmer just until the cheese melts and the chicken is cooked through, about 2 minutes more
Can be served with cooked spagetti or as is with a salad on the side-YUM