Preheat oven to 350°. Spread about 1 cup tomato sauce in the bottom of a medium baking dish.
Using a spoon, hollow out the eggplants leaving about a 1/2” thick border around skin to create a boat. Roughly chop scooped out eggplant. Place eggplant boats on prepared baking dish.
In a large skillet over medium heat, heat olive oil. Add onion and cook until softened, about 5 minutes.
Stir in chopped eggplant and season with oregano, salt and pepper. Cook, stirring often, until the eggplant is golden, about 3-5 minutes.
Stir in garlic and cook until fragrant, about 30 seconds. Transfer mixture to a bowl.
To the bowl with the eggplant mixture, add chopped tomatoes, egg, 1 1/2 cups shredded mozzarella, and 1/2 cup tomato sauce. Mix until just combined. Scoop mixture into eggplant boats.
Top with the remaining cup of mozzarella cheese, Top with 1 1 cup of Parmesan and the bread crumbs.
Bake until the eggplants are tender and the cheese has melted, about 40 minutes. Just before the eggplants are done, slice the basil into thin strips (this is called a chiffonade)
Garnish eggplants with basil and serve