Preheat the oven to 425°F and place a rack in the upper third; line a rimmed baking sheet with aluminum foil.
Make the breadcrumbs: In a food processor combine torn whole-wheat bread, grated Parmesan, and olive oil; add a pinch of salt and pepper and pulse until coarse crumbs form. Transfer crumbs to a shallow bowl.
Prepare dredging stations: place the flour in a second shallow bowl and season with salt and pepper; put the beaten egg white in a third shallow bowl.
Bread the chicken: Dip the top side of each chicken breast in flour, shaking off excess, then dip that same side in the egg white, letting excess drip, and press the breadcrumb mixture onto that side only. Repeat with remaining breasts and arrange breaded-side up on the prepared baking sheet.
Bake the chicken for 8 to 10 minutes, until breadcrumbs are crisp and browned; remove from oven and sprinkle the tops with shredded mozzarella, then return to the oven for 2 to 4 minutes until chicken is opaque and cheese is lightly browned.
While the chicken bakes, make the sauce: in a large skillet add the canned tomatoes (break them up with your fingers), minced garlic, and salt and pepper to taste. Bring to a boil, then reduce to a simmer and cook until slightly thickened, about 6 to 8 minutes.
To serve, spoon a generous amount of tomato sauce over each chicken breast and garnish with chopped fresh basil if desired.
