Heat 2 tablespoons of the oil in a large saucepan over medium-high heat. Add the celery and cook for 3 minutes. Stir in the eggplant and tomatoes.
In a small bowl, combine the tomato paste, vinegar, ¼ cup water, 2 ½ teaspoons salt, ¼ teaspoon pepper, and the sugar. Stir into the eggplant mixture.
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 desired), and parsley.
Meanwhile, cook the penne according to the package directions. Toss with the remaining oil; let cool. Combine with the eggplant mixture and serve.