Stir the bread crumbs, 1 cup of Parmesan and 1 teaspoon of salt in a medium bowl to blend. Dip the cheese in the eggs to coat completely and allow the excess egg to drip back into the bowl. Coat the cheese in the bread crumb mixture, patting to adhere and coat completely. Place the cheese sticks on a baking sheet. Repeat dipping the cheese sticks in the egg and bread crumb mixture to coat a second time. Cover and freeze until frozen, about 2 hours and up to 2 days.
Heat the oil in a large frying pan over medium heat. Working in batches, fry the cheese until golden brown, about 1 minute per side. Transfer the fried cheese to plates. Sprinkle with the remaining cheese and serve with the Marinara Sauce.
In a large casserole pot, heat the oil over a medium-high flame. Add the onions and garlic and saute until the onions are translucent, about 10 minutes. Add the celery, carrots, and 1/2 teaspoon of each salt and pepper. Saute until all the vegetables are soft, about 10 minutes. Add the tomatoes and bay leaves, and simmer uncovered over low heat until the sauce thickens, about 1 hour. Remove and discard the bay leaf. Season the sauce with more salt and pepper, to taste. (The sauce can be made 1 day ahead. Cool, then cover and refrigerate. Rewarm over medium heat before using.)