Preheat oven to 425°F. Sprinkle eggplant slices on both sides with 1/4 teaspoon of the salt, and place in a colander to drain 15 minutes. Rinse well, and press between 2 clean, absorbent towels to dry. Arrange eggplant slices in a single layer on greased baking sheets. Rub eggplant slices on both sides with 3 tablespoons of the oil. Bake in preheated oven until just beginning to brown, 13 to 15 minutes. Remove eggplant from oven, and reduce oven temperature to 375°F.
While eggplant is baking, stir together ricotta, chopped basil, pepper, and remaining 3 tablespoons oil and 1/2 teaspoon salt in a medium bowl. Pour 1 cup of the marinara into an 11- x 7-inch baking dish. Place 1 tablespoon ricotta mixture on 1 eggplant slice, and roll up from 1 short end. Place rollup, seam side down, in baking dish. Repeat with remaining ricotta mixture and eggplant slices. Top evenly with remaining 1/4 cup marinara.
Bake at 375°F until sauce is bubbly and warm and tops of rollups are very lightly browned, 15 to 20 minutes. Top with shaved Parmesan cheese and chopped basil. Serve immediately.