Preheat the oven to 450ºF. Arrange the zucchini in single layers on two Silat- or parchment-lined rimmed sheet pans. Season with salt and pepper on each side, drizzle each pan with 1 tablespoon olive oil, toss to coat, then spread into an even layer. Roast for 10 minutes. Remove pans from oven and set aside.
Reduce oven to 400ºF.
Meanwhile, make the breadcrumb topping: toss the breadcrumbs with the 1/3 cup grated parmesan cheese, remaining 2 tablespoons oil, 1/2 teaspoon salt and pepper to taste. Set aside.
Into a circular gratin dish (about 9 inches in diameter) or a 9-by-9-inch or similar baking pan, spoon a small amount of sauce (about a heaping 1/3 cup), then add a thin scattering of parmigiano, then a single layer of zucchini, shingling the slices slightly. Repeat until all ingredients are used, ending with a little sauce and cheese—you should have about 3 layers of zucchini. Top with the breadcrumb mixture.
Bake until the mixture is bubbly and top is golden, 25 minutes or so depending on size of pan and thickness of layers. Remove from heat and allow to rest for 10 minutes before serving. This also tastes great at room temperature.