In a large saucepan over medium heat, sauté onion and salt in oil 5 minutes. Stir in chicory and garlic; sauté 10 minutes or until greens are tender.
Gently break eggs over greens. Cover saucepan and reduce heat to low. Cook until whites are done through and yolks are slightly runny, 5-7 minutes.
Using a large spoon, carefully scoop up each egg with a portion of greens and place in a pasta dish. Sprinkle with cheese and black pepper to taste.