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.
Cut chicken breasts in half to make 6–8 large, thin cutlets.
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.
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.