Thinly slice the eggplant into rounds and season with salt. Pour some flour into a shallow dish. Beat the eggs in another dish. In a third dish, mix the breadcrumbs and Parmesan. Dredge the eggplant in the flour, then dip in the eggs and coat with the breadcrumb mixture.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Working in batches, cook the eggplant until golden, about 2 minutes per side, adding more oil between batches, if necessary. Drain on paper towels and season with salt.
Toss the tomatoes with the remaining 2 teaspoons olive oil and the vinegar in a small bowl. Spoon some ricotta onto each eggplant slice. Top with the tomato mixture and basil.