Stir the oil and herbs in a small bowl to blend. Season with salt and pepper. Brush both sides of the cutlets with the herb oil. Heat a heavy large oven-proof frying-pan over high heat. Add the cutlets and cook just until brown, about 2 minutes per side. Remove the pan from the heat.
Spoon the tomato sauce over and around the cutlets. Sprinkle one teaspoon of mozzarella over each cutlet, then sprinkle two teaspoons of Parmesan over each. Sprinkle the butter pieces on top of the cutlets. Bake until the cheese melts and the chicken is cooked through, about 3 to 5 minutes.
For the Simple Tomato Sauce:
In a large casserole pot, heat oil over medium high heat. Add onion and garlic and saute until soft and translucent, about 2 minutes. Add celery and carrots and season with salt and pepper. Saute until all the vegetables are soft, about 5 minutes. Add tomatoes, basil, and bay leaves and simmer covered on low heat for one hour or until thick. Remove bay leaves and check for seasoning. If sauce still tastes acidic, add unsalted butter, one tablespoon at a time to round out the flavors.
Add half the tomato sauce into the bowl of a food processor. Process until smooth. Continue with remaining tomato sauce. If not using all the sauce, allow it to cool completely and pour 250ml-500ml portions into freezer plastic bags. This will freeze up to 6 months. Makes about 1.5L.