Preheat oven to 425°F, with rack in upper third. Line a rimmed baking sheet with aluminum foil; set aside.
In a food processor, place the bread, Parmesan, oil and a pinch each of salt and pepper. Pulse until coarse crumbs form; transfer to a shallow bowl. Place the flour in a second shallow bowl; season with salt and pepper. Place the egg white in a third shallow bowl, and beat with a fork until frothy.
Dip the top side of the chicken breast in flour, shaking off excess. Dip the same side in egg white, letting excess drip off, then in breadcrumbs, pressing to adhere. (Do not bread other side.) Repeat with remaining chicken and transfer, breaded side up, to your prepared baking sheet. Bake until the breadcrumbs are crisp and browned, 8 to 10 minutes. Remove from the oven; sprinkle with mozzarella. Continue baking until chicken is opaque throughout and cheese is lightly browned, 2 to 4 minutes.
Meanwhile, in a large skillet, add the tomatoes, breaking them up with your fingers. Add the garlic; season with salt and pepper. Bring to a boil, reduce to a simmer, and cook until the sauce has thickened, 6 to 8 minutes. Serve the chicken topped with a generous amount of tomato sauce. Garnish with basil, if desired.