Heat 1 tablespoon oil in a skillet over medium heat. Stir in the onion and cook until golden brown. Set aside.
Heat 1/2 tablespoon oil in the skillet. Season pork chops with salt, pepper, and garlic powder, and place in the skillet. Cook to desired doneness. Set aside and keep warm.
Heat remaining oil in the skillet. Return onions to skillet, and stir in tomatoes, garlic, and basil. Cook and stir about 3 minutes, until tomatoes are tender. Mix in balsamic vinegar, and season with salt and pepper. Top chops with the onion and tomato mixture, and sprinkle with feta cheese to serve.