Preheat oven to 500°.
Combine eggplant and oil in a jelly-roll pan. Bake at 500° for 12 minutes, stirring once.
While eggplant bakes, cook pasta according to package directions, omitting salt and fat. Drain pasta in a colander over a bowl, reserving 1/2 cup cooking liquid.
Combine the oregano, chickpeas, and tomatoes in a large skillet over medium heat; cook 4 minutes. Stir in eggplant and pasta. Combine reserved 1/2 cup cooking liquid and egg in a small bowl; stir well with a whisk. Add egg mixture to pan; stir well. Cook over low heat 5 minutes or until egg mixture is slightly thick, stirring constantly (do not boil). Stir in feta, salt, and pepper. Serve immediately.