Prepare a charcoal grill with a single layer of hot coals, set a gas grill to medium-high heat, or heat a stovetop grill pan over medium-heat high. Slice the eggplant into 1/2-inch rounds, brush the eggplant slices generously with olive oil, sprinkle with salt and pepper, and grill for 3-5 minutes on each side, until charred and cooked through. Set aside to cool. Once the eggplant has cooled, cut each slice into 1-inch pieces. Alternatively, you can dice the eggplant into ¾-inch pieces, toss with 2 tablespoons olive oil, sprinkle with salt and pepper, and roast for 25-30 minutes at 400 degrees, tossing occasionally, until softened and browned.
Meanwhile, bring a large pot of salted water to a boil, and begin the sauce. In a very large (12-inch) sauté pan or a Dutch oven, combine the raisins and vinegar and cook over low heat until the vinegar has completely evaporated, about 5 minutes. Transfer to a small bowl and set aside.
In the same pan, heat the olive oil, tomatoes, garlic, anchovy paste, red pepper flakes, and 1½ teaspoons salt over medium heat. Bring to a simmer, then turn the heat to medium-low and cook for 10 to 15 minutes, stirring occasionally, until the tomatoes have burst and are starting to break down. Add the eggplant and the raisins and cook for 5 more minutes.
Cook the pasta according to the directions on the package. Drain and add to the sauce (or transfer everything to the pasta pot if you need more room.) Add the pine nuts and parsley, reserving about 2 tablespoons of each for the top, and toss gently. Sprinkle the pasta with the reserved pine nuts and parsley, sprinkle lightly with salt, and serve.