Preheat oven to 425 degrees F.
Cut eggplant in half and score flesh in a crisscross pattern. Drizzle flesh with 2 tablespoons olive oil and season with salt and pepper. Place eggplant on baking sheet and cover with foil. Roast for 35-40 minutes or until eggplant is soft and tender. Remove pulp with spoon and set aside.
Heat 1 tablespoon oil in a large pot over medium heat. Add chopped onion and saute until tender, about 5 minutes. Add garlic and saute for 1 more minute.
Pour white wine and simmer for 1 minute. Add canned tomatoes, chicken or vegetable stock, oregano, basil, balsamic vinegar, parmesan rind, and eggplant pulp. Bring to a boil, then reduce heat to low and simmer for 30 minutes.
Meanwhile, make garlic bread crisps. Drizzle remaining 2 tablespoons oil on thinly sliced baguette, tossing to coat. Spread bread on baking sheet in an even layer and bake for 8-10 minutes or until golden brown, flipping bread over halfway through. Remove from oven and rub garlic clove directly on bread. Let cool.
Transfer half of the soup to a blender and blend until smooth. Pour soup back into pot and add breadcrumbs. Stir to combine and simmer for 5 more minutes. Season with salt and pepper.
Portion soup into bowls and top with garlic bread crisps, fresh basil, parmesan, and freshly cracked black pepper. Serve immediately.