For the sauce, heat 1 tablespoon of the oil in a large skillet over medium-low heat. Add the onion, garlic and 1/2 teaspoon salt. Cook, stirring, 1 minute. Cover, reduce heat to very low and cook until vegetables are softened, about 5 minutes. (Check a few times during cooking; if vegetables begin to brown, add 2 teaspoons water and stir.) Add the tomatoes with juice, basil and another 1/2 teaspoon salt. Bring to a simmer, cover and simmer gently 5 minutes. Then simmer very gently, partially covered, until thickened, about 20 minutes. Season with 1/8 teaspoon pepper.
Meanwhile, using a mandoline or vegetable peeler, slice the zucchini lengthwise into 1/8-inch-thick long pappardelle-like strips, turning the zucchini and slicing on 4 sides only until you see the center seeds. Discard the centers.
Remove the tomato sauce to a bowl with a rubber spatula; no need to clean the skillet. Heat the remaining 1 tablespoon of oil in the skillet over medium heat. Add the zucchini and 1/4 teaspoon salt. Cover and cook until wilted, tossing often with tongs for even cooking, 8 to 10 minutes. Return the tomato sauce to the pan, add 1 tablespoon of the parsley, and season with 1/8 teaspoon pepper; cover and set aside.
On a plate, combine the bread crumbs, 1/4 cup grated Parmesan and the remaining chopped parsley. Place the egg white on a second plate. Sprinkle chicken on both sides with salt and pepper. Dip the chicken into the egg whites, and then into the bread crumb mixture to coat completely; set aside on a large plate or platter.
Heat 2 teaspoons oil in each of two nonstick 10-inch skillets over medium-high heat. Add half of the chicken to each skillet and cook until lightly browned on one side, 2 to 3 minutes. Flip, and cook until chicken is firm, and lightly browned on the other side, 1 to 3 more minutes.
To serve, re-warm the zucchini in the tomato sauce over medium heat. Use tongs to make a “twist” of zucchini pappardelle on each of 4 plates. Lean chicken cutlets against the side of zucchini. Scoop 1 tablespoon ricotta onto each plate, and spoon remaining tomato sauce on top of the chicken. To garnish each plate, drizzle chicken with 1/2 teaspoon olive oil, and sprinkle with 1 teaspoon Parmesan.