Heat 2 tablespoons of the oil in a large saucepan over medium-high heat. Add the celery and cook, 3 minutes. Stir in the eggplant and tomatoes.
In a small bowl, combine the tomato paste, vinegar, 1/4 cup water, 2 1/2 teaspoons salt, 1/4 teaspoon pepper, and the sugar. Stir into the eggplant. Cover and reduce heat to medium-low. Cook, stirring occasionally, until the eggplant is tender, 15 to 20 minutes. Remove from heat and stir in the capers, pine nuts (if using), and parsley.
Meanwhile, cook the penne according to the package directions. Toss with the remaining oil, let cool, and cover. Combine the eggplant with the pasta and top with grated Parmesan before serving.