Preheat oven to 450°. Lightly grease a 9”x13” baking dish with olive oil and set aside.
In a bowl, combine crostini, oregano, paprika and season with pepper and transfer to a shallow plate or pie pan. Set aside.
Cut each breast horizontally into 2 even pieces. Place split breast halves between 2 pieces of plastic wrap and pound lightly with a mallet until they are a uniform ½” thickness. Remove chicken from plastic wrap and place on a sheet pan or platter; repeat with remaining breasts.
In a heavy-bottomed frying pan over medium heat, add olive oil and 1 tablespoon of butter. Place flour in another shallow pie plate and liberally season with salt and pepper.
In another shallow plate, combine eggs with 1 tablespoon of water and beat until frothy.
Place coating mixture in a line with flour and eggs. Working with 1 cutlet at a time, dredge both sides of chicken in seasoned flour, and then dip them in egg wash to coat completely, letting excess drip off, then dredge in coating mixture.
Place cutlet directly into heated pan and continue coating remaining cutlets, being sure not to crowd pan (typically no more than 4 cutlets at one time). Fry cutlets until golden brown and crusty, about 3 minutes per side, adjusting heat as necessary. Once browned, remove cutlets from pan and place, slightly shingled, into prepared casserole dish. Repeat above steps with second round of cutlets adding remaining oil and butter to pan as needed.
Once all cutlets have been browned, place a slice of fresh mozzarella atop each cutlet and sprinkle with grated parmesan. Ladle 1 cup of tomato sauce over chicken and bake cutlets in the oven until cheese is bubbly, 8-10 minutes. Garnish with basil prior to serving.