Arrange eggplant on paper towels; salt both sides. Stand 20 minutes; pat dry to remove moisture.
Preheat oven to 400°F; line two baking sheets with parchment. Mix breadcrumbs and 1/2 cup Parmesan in shallow bowl.
Dip eggplant in eggs, then crumbs; arrange on sheets and spray with oil. Bake 25 minutes, flipping halfway.
Spread 1 cup marinara in 9x13-inch dish bottom; layer half the eggplant, half the remaining sauce, half the mozzarella, and half the remaining Parmesan.
Repeat with remaining eggplant, sauce, and cheeses; sprinkle with oregano.
Reduce oven to 375°F; bake casserole 30 minutes until cheese is bubbly and golden. Rest 10 minutes; garnish with basil and serve.