Cut fingerling potatoes (or small red potatoes) into halves or quarters, depending on thickness of fingerlings—thin, small fingerlings may also be left whole, larger potatoes should be quartered to speed cooking process. Cover a large cookie sheet with foil. Place potatoes on cookie sheet. Combine with peppers and onions, garlic and crushed red pepper flakes. Coat the potatoes, peppers and onions with extra-virgin olive oil—just enough to coat vegetables in a thin layer, 2 to 3 tablespoons. Season liberally with salt and pepper. Place potatoes in the oven and roast 20 to 22 minutes, until potatoes are just tender and peppers and onions are crisp at edges. Toss mixture with tongs, turning the potatoes after 15 minutes. When the potatoes are cooked, transfer them to a serving dish.
While potatoes cook, prepare chicken. 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. 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 and serve with potatoes, peppers and onions.