Preheat the oven to 400 degrees. Line a large baking sheet with parchment paper or foil.
To make the marinara sauce, heat the oil in a medium saucepan over medium heat. Add the onion and cook for 3 minutes, until soft. Add the garlic and Italian seasoning and cook for 30 seconds, until the herbs are fragrant. Add the tomato sauce and sugar (if using) and bring to a simmer.
Reduce the heat to low, partially cover and simmer for 10 minutes. Season to taste with salt and black pepper.
Meanwhile, to prepare the chicken, in a shallow dish, combine the flour, 1 teaspoon of salt, and 1/4 teaspoon black pepper. Mix well.
In a second shallow dish, whisk together the eggs and Italian seasoning until light and frothy.
In a third shallow dish, combine both breadcrumbs, 1/4 cup of the parmesan cheese, and garlic powder.
Pat the chicken cutlets dry with a paper towel. Add the chicken to the flour mixture and turn to coat completely (coat every nook and cranny). Shake off excess flour.
Transfer the chicken to the eggs and turn to coat. Use your fingers to slide excess egg from the chicken.
Transfer the chicken to the breadcrumb mixture and turn to coat. Gently press the breadcrumbs into the chicken to make sure they stick.
Heat the oil and butter together in a heavy skillet over medium-high heat. When the butter has melted, and the temperature has reached 325 degrees, add the chicken in batches (two cutlets at a time). Fry for 2 to 4 minutes per side, until browned and crisp. Remove the chicken with a slotted spatula and transfer to a wire rack.
Transfer the chicken to the prepared pan and top with the sauce, about 1/4 cup sauce per cutlet (reserve any extra sauce for serving). Top with the mozzarella cheese and remaining 1/4 cup of parmesan cheese.
Bake for 15 to 20 minutes, until the chicken is cooked through (165 degrees on a meat thermometer) and the cheese melts. If desired, place the pan under the broiler to brown the cheese.
Top with parsley or basil and serve immediately.