Preheat the oven to 350 degrees.
Begin by making the Brown Butter Tomato Sauce: in a Dutch oven heat the butter on low heat and cook until the butter turns light brown. Add the onions and one tablespoon of the garlic and cook until they're soft. Add the tomatoes, sugar, a tablespoon of the oregano, chicken stock, a half teaspoon of the kosher salt, and a quarter teaspoon of red pepper flakes. Simmer uncovered while you fry the chicken.
Split each breast in half, so that you have 4 thin cutlets. Using a meat pounder, pound them even thinner. Prepare a dredging station with three bowls: fill the first bowl with the flour and a quarter teaspoon each of salt and pepper. Fill the second bowl with the eggs. Fill the third bowl with the breadcrumbs, a quarter teaspoon each of the kosher salt and red pepper flakes, a tablespoon of the minced garlic, the herbs, and one cup of the Parmesan.
Heat a cast iron skillet with a quarter inch of the vegetable oil on medium high heat. The oil is ready when a small piece of chicken sizzles immediately. Dip each piece of chicken in each of the three bowls- first flour, then eggs, and finally breadcrumbs. Fry two cutlets at a time until they're golden brown on each side and cooked through. Drain the chicken on a wire rack over a baking dish.
When all the chicken is cooked. Top them with a spoonful of sauce (you can freeze the rest of the sauce). Then sprinkle on mozzarella, and a half cup of the parmesan cheese. Bake until the cheese is melted, about 5 minutes.