1. Preheat oven to 375 degrees. Preheat a grill pan over medium-high heat.

2. Stir olive oil and vinegar together in a small bowl and brush onto both sides of the eggplant slices; season both sides with salt and pepper. Grill eggplant slices, turning once, until tender and golden brown, 3 to 4 minutes per side. Transfer eggplant slices to a rimmed baking sheet with the short ends facing you.

3. In a medium bowl, stir together ricotta, Parmesan, and half of the basil; season with salt and pepper. Spoon about 3 tablespoons of the cheese mixture onto each slice of eggplant and 1 inch from the bottom edge, leaving a 1/4-inch border on each side. Roll each slice away from you and arrange rolls, seam side down, on the baking sheet. Spoon tomato sauce over rolls and place them in the oven until warmed through, about 15 minutes. Sprinkle with Parmesan and remaining basil; serve immediately.