Roll out a 2-foot piece of waxed paper or foil near the stove top.
Heat a large nonstick skillet over medium high heat -- your pan must be very hot when the chicken is added.
Pile the shredded cheese on the work surface created with the waxed paper or foil.
Season your chicken breasts with black pepper but no salt; the cheese will add enough salt to the taste of the dish.
Press the breasts firmly into the cheese. Coat both sides of breasts with as much cheese as possible.
Add 1 tablespoon extra-virgin olive oil to the skillet, 1 turn of the pan. Set breasts into the skillet and cook 7 minutes on each side, until cheese forms an even, golden casing around the tender chicken breasts.
While chicken cooks, combine chopped tomatoes with basil in a small bowl. Season with salt and pepper, to your taste.
Drain off any excess oil from chicken as you remove it from the skillet. Top chicken with big spoonfuls of raw sauce.