Put each chicken breast between to pieces of plastic wrap and pound them out to a uniform thickness, no more than about 1/3-inch.
In a large bowl, whisk together the 1 1/2 teaspoons salt, bread crumbs, oregano, thyme, and season with pepper.
Place the flour in a large plate or bowl. In another medium bowl, whisk the egg and milk together. Dredge a chicken breast in the flour and shake off excess. Then dip it into the egg mixture and finally dredge in the seasoned breadcrumb mixture. Shake off any excess breading and transfer to a baking sheet. Repeat with the remaining chicken.
Preheat the oven to 400 degrees F.
In a large straight-sided skillet, pour the vegetable oil to a depth of 1/2-inch. Heat the oil over medium heat until it registers 400 degrees F on a deep-frying thermometer. (The oil must be heated to 400 degrees F so that the breaded chicken, when added, will drop the temperature of the oil to the proper frying temperature of 375 degrees F.)
Fry 1 breast at a time until golden brown on each side, about 6 minutes total. Using tongs, transfer to a paper towel-lined baking sheet and season with salt, to taste.
Lightly brush a baking dish, large enough to place the chicken in a single layer, with olive oil. Cover the bottom of the baking dish with half of the marinara sauce and arrange the chicken over the sauce. Cover with the remaining sauce. Scatter the Parmesan and the mozzarella on top. Bake until sauce is bubbling and the cheese is brown, about 30 minutes. Serve immediately.
Heat the oil in a medium saucepan over medium-high heat. Saute the onion, garlic, and Italian seasoning. Stir until lightly browned, about 5 minutes. Add the tomatoes and bring to a boil. Lower the heat to a simmer, cover, and cook for 10 minutes.
Stir in the salt and season with pepper, to taste. Use immediately or store covered in the refrigerator for up to 3 days or freeze for up to 2 months.
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