Preheat oven to 450 degrees. In a colander, toss eggplant with 2 teaspoons salt. Let stand 30 minutes. Arrange in a single layer on a clean kitchen towel and roll up tightly to extract excess water; transfer to a rimmed baking sheet. Toss with 1 tablespoon oil, and garlic; and season with pepper. Bake until golden and cooked through, 30 to 35 minutes. When cool enough to handle, peel garlic cloves.
Meanwhile, In a large pot of boiling salted water, cook pasta according to package instructions. Reserve 1/2 cup pasta water, drain. Return pasta to pot then add eggplant, peeled garlic cloves, radicchio, currants, olives, remaining 1 tablespoon oil, and enough pasta water to create a light sauce that coats the pasta. Top with Parmesan to serve.