Place breadcrumbs in a large skillet over medium-high heat. Stir around occasionally until breadcrumbs are golden-brown and crispy, about 7 minutes. Transfer to a small bowl and set aside.
In a shallow bowl, combine flour, salt, and pepper. With a sharp knife, carefully chicken breasts in half along the length and dredge chicken in flour mixture.
In same skillet, heat 2 tablespoons oil over medium-high heat until shimmering. Working in batches, cook chicken in oil, turning occasionally until chicken registers 160F, using additional oil as needed. Transfer cooked chicken to a plate and cover with aluminum foil.
Pour crushed tomatoes into same skillet along with garlic, basil and salt and pepper to taste. Stir occasionally until tomatoes are simmering. Reduce heat to low and nestle cooked chicken breasts into sauce and sprinkle with toasted breadcrumbs. Top with cheeses and additional basil if desired. Cover skillet and let stand 5-10 minutes or until cheese is melted. Serve chicken immediately.