In a food processor, puree tomatoes; transfer to a medium saucepan and stir in olive oil. Bring to a boil; reduce to a simmer and cook until thickened, 30 minutes. Season tomato sauce with salt and pepper.
Meanwhile, in a colander, toss eggplant with 1 1/2 teaspoons salt. Let stand 30 minutes. Press slices between a double layer of paper towels to dry. Dredge eggplant in flour (shaking off excess), then dip in eggs (allowing excess to drip off), and sprinkle lightly with breadcrumbs.
Preheat oven to 375 degrees. Place a wire rack on a rimmed baking sheet; set aside. In a large skillet, pour enough vegetable oil to come halfway up side. Heat oil over medium-high until pinch of breadcrumbs dropped in skillet sizzles. In batches, fry eggplant until golden, 2 to 3 minutes per side; transfer to rack to drain.
Spread 1 cup tomato sauce in a 9-by-13-inch baking dish. Layer half the eggplant over sauce and sprinkle with 1/4 cup Parmesan. Top with 1 1/2 cups sauce, then remaining eggplant. Finish with remaining sauce, 1/4 cup Parmesan, and mozzarella. Bake until lightly browned and bubbling, 40 to 45 minutes.
To Freeze: Assemble dish but do not bake; wrap tightly with foil and freeze, up to 3 months. Thaw completely, then bake as directed.