Preheat the oven to 450°F and position 2 racks evenly.
Arrange the eggplant slices in a single layer on rimmed baking sheets and brush both sides with the olive oil.
Season both sides of the eggplant with dried oregano, kosher salt, and freshly ground black pepper.
Bake the eggplant for 15 minutes, flip the slices, then bake about 10 minutes more until lightly browned; set aside and reduce oven temperature to 400°F.
Bring a large pot of salted water to a boil and cook the lasagna sheets for about 4 minutes until still fairly firm, then drain and rinse with cold water.
Layer the cooked noodles on a parchment-lined baking sheet with parchment between layers to prevent sticking.
In a mixing bowl combine the ricotta, 3 ounces of the mozzarella, 1 1/2 ounces of the Parmesan, and the chopped basil; season with salt and pepper to taste.
Spread 3/4 cup of tomato sauce in the bottom of a 9 x 13-inch baking dish.
Assemble the lasagna: place 1/4 of the lasagna sheets in an even layer over the sauce, top with one-third of the roasted eggplant, then one-third of the ricotta mixture; repeat two more times with sauce, noodles, eggplant, and ricotta mixture.
Finish with the remaining lasagna sheets, spread the remaining 3/4 cup tomato sauce on top, then sprinkle with the remaining 4 ounces mozzarella and 1 1/2 ounces Parmesan.
Cover the dish with foil and bake at 400°F for 40 minutes, then remove the foil and bake about 15 minutes more until the cheese is melted and golden.
Let the lasagna rest for 10 minutes before slicing and serving.