Using a food processor, finely chop the eggplant. In a large nonstick skillet, heat 11/2 tablespoons olive oil over medium-high heat. Add 1 clove garlic and cook until golden, 1 to 2 minutes. Add the eggplant, season with salt and pepper and cook, stirring, until browned, about 10 minutes. Transfer to a large bowl and let cool for 5 minutes. Stir in the mozzarella and 1/3 cup parmesan.
In the same skillet, heat 3 tablespoons olive oil over medium heat. Add the remaining 2 cloves garlic and cook until golden, 1 to 2 minutes. Stir in the tomatoes and cook until softened, about 4 minutes; season with salt and pepper. Lower the heat to low and stir in the basil.
Bring a large pot of salted water to a boil, then add the remaining 2 tablespoons olive oil. Working with 1 at a time, fill each wrapper with 2 rounded tablespoons of the eggplant mixture; moisten the edges with water and fold in half, pressing the edges to seal. Working in 2 batches, cook the ravioli until tender, about 4 minutes. Using a slotted spoon, transfer 3 ravioli each to 4 shallow bowls. Stir 1/2 cup of the pasta cooking water into the tomato sauce and season with salt and pepper; spoon over the ravioli and sprinkle the remaining parmesan on top.