Heat 1 tablespoon olive oil in a skillet over medium heat. Stir in onion and cook until golden brown; transfer onion to a plate and set aside.
Heat 1/2 tablespoon olive oil in the skillet. Season pork chops with salt, pepper, and garlic powder; place in the skillet and cook to desired doneness. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C). Set aside and keep warm.
Heat remaining olive oil in the skillet; add cooked onion, tomatoes, garlic, and basil. Cook and stir until tomatoes are tender, about 3 minutes. 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.