Cut zucchini lengthwise into 1/4-inch thick slices with a knife or mandolin.
Pour 2 tablespoons tomato sauce on the bottom of a 9x13-inch baking dish. Arrange zucchini slices in a single layer, slightly overlapping, over tomato sauce.
Top with a thin layer of mozzarella, 1/3 of the bechamel (see Editor's Note), 1/3 of remaining tomato sauce, 1/3 of the Parmigiano Reggiano cheese, and 1/3 of the basil. Repeat layers, topping with bechamel and Parmigiano Reggiano cheese.
Bake in the preheated oven until sauce is bubbly and the top is golden brown, about 35 minutes. Allow to set until remaining liquid is absorbed, about 10 minutes.
