Transfer eggplant to prepared sheet. Toss with 2 tablespoons oil. Roast eggplant until tender, stirring occasionally, about 30 minutes. Set aside. Maintain oven temperature.
Mix ricotta cheese, 1/2 cup Parmesan, shallots and rosemary in large bowl. Season with salt and pepper.
Oil 13 x 9 x 2-inch glass baking dish.
Spread 1/2 cup tomato sauce in dish. Arrange 3 lasagna noodles crosswise in single layer in dish.
Spread half of ricotta mixture over noodles. Arrange half of eggplant over.
Sprinkle with salt and pepper. Spoon generous 1 cup sauce over. Arrange half of mozzarella over sauce. Repeat layering 1 more time. Top with 3 lasagna noodles.
Spread remaining sauce over.
Sprinkle with 3/4 cup Parmesan. Cover tightly with lightly oiled foil. (Can be made 1 day ahead; chill.)
Bake until noodles are tender and lasagna is heated through, about 45 minutes. Uncover; bake until cheese begins to brown and sauce is bubbling slightly at edges, about 15 minutes longer.