Set a wire rack inside a rimmed baking sheet. Line another baking sheet with foil. Cut two 12-inch sheets of plastic wrap.

Cut chicken breasts in half lengthwise into 4 pieces. Place one piece on plastic, cover with another sheet, and pound until 1/4-inch thick. Transfer to rack. Repeat. Season with salt and pepper.

Put flour in a pie plate. Dredge chicken in flour and return to rack.

Mix breadcrumbs, 1/4 cup Parmesan, salt, and pepper in a bowl. Whisk milk and egg in another bowl. Dip chicken in milk mix and coat in breadcrumbs. Refrigerate for at least 30 minutes.

For the sauce, heat 1/3 cup oil in a pot. Add garlic, oregano, and red pepper; cook for 1 minute. Add tomatoes, basil, and salt. Bring to boil, reduce heat, and simmer for 30 minutes. Smash tomatoes and season.

In a skillet, heat 1/2 cup oil. Cook 2 cutlets until golden brown, about 1 minute per side. Transfer to the foil-lined sheet. Repeat with remaining cutlets.

Preheat broiler. Place chicken on a baking sheet, top with sauce, Parmesan, and mozzarella. Broil until cheese melts and browns, 2 to 3 minutes.

Meanwhile, boil salted water and cook spaghetti until al dente. Drain and add to the sauce. Stir to coat pasta. Serve with chicken and basil.