Preheat oven to 400°F. Lightly spray a baking sheet with spray oil. Beat eggs with 1 tablespoon water in shallow bowl. Place breadcrumbs on small plate.

Dredge eggplant slices in egg mixture, then in breadcrumbs. Lay eggplant in a single layer on the baking sheet (slightly overlapping is fine). Drizzle eggplant with 2 tablespoons olive oil and sprinkle with salt.

Bake eggplant until crisp and golden, about 20 minutes. Remove from oven and flip eggplant slices. Drizzle with 2 tablespoons olive oil. Bake approximately 20 minutes more or until golden. Set aside. Reduce oven temperature to 350°F.

Heat a large skillet with remaining 1 tablespoon olive oil over medium heat. Add mushrooms and cook until softened, about 4 minutes. Turn off heat and combine mushrooms with marinara.

Lightly spray a casserole dish with spray oil. Cover bottom of dish with about half of the marinara. Top with a layer of eggplant slices, then drop half of the ricotta by spoonfuls over the eggplant. Srinkle about half of the mozzarella and Parmigiano-Reggiano over the ricotta. Repeat with remaining marinara, eggplant, ricotta, mozzarella and Parmigiano-Reggiano. Transfer to the oven and bake until the mixture is bubbly and heated through, about 45 minutes.

To freeze, assemble dish but do not bake. Wrap tightly with foil and freeze, up to 3 months. When ready to eat, thaw completely, then bake as directed.