Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper. Pour bread crumbs in a shallow bowl.
Dip eggplant into eggs; coat with gluten-free bread crumbs. Place in a single layer on prepared baking sheet; lightly sprinkle with Parmesan cheese.
Bake in the preheated oven for 6 minutes; remove from oven. Flip eggplant with a spatula; brush with olive oil. Bake until golden brown, about 6 minutes. Remove from oven; reduce heat to 350 degrees F (175 degrees C).
Spread enough spaghetti sauce into a 7×11-inch baking pan to cover the bottom; layer on some of the eggplant slices. Sprinkle mozzarella cheese over eggplant; top with Parmesan cheese. Repeat layering sauce, eggplant, mozzarella cheese, and Parmesan cheese in this order; top with basil.
Bake in the preheated oven until cheese is bubbly and lightly golden, about 25 minutes.