Cut the potatoes into small cubes and boil until firm/tender. Drain well. Bring a pot of water to a gently simmer to cook the eggs. While this occurs, heat the oil in a large skillet over medium heat. Add the potatoes, onion, bell pepper, corned beef, thyme, salt and pepper and cook 5 minutes, then reserve on low heat. Add a drop of white vinegar to the water and swirl the water with a spoon. Add the eggs and cook to the desired doneness. Divide the corned beef hash among 4 plates, top each with an egg and serve.