1. In a large soup pot, simmer split peas, water, bay leaf and salt for three to four hours. Check every so often to make sure water is just covering split peas, and add more water if necessary (you may need up to four cups additional water). Split peas should be soft and starting to melt.
2. While soup is cooking, make pastrami hash. Combine potatoes, corned beef, onion, bell pepper, thyme and ground pepper in a bowl; toss to mix. Heat oil in a heavy medium skillet over medium heat. Add potato mixture; press to flatten with a spatula.
3. Cover and cook until bottom begins to crisp, about five minutes. Using a metal spatula, turn over browned bottom in sections.
4. Cook, uncovered, until hash is thoroughly flecked with brown bits and onion and bell pepper are tender, turning over browned bottom in sections two more times, about 10 minutes longer. Turn off heat and set aside until ready to use. Reheat before serving, if necessary.
5. Toward end of cooking time for split peas, start cooking vegetables for the soup. In a large skillet, heat oil over medium-high heat. Add onion, celery, carrots, garlic and potato and cook until tender, about 10 minutes.
6. Add to split peas and heat to blend flavors, stirring occasionally. Add red wine, thyme, dry mustard, and sesame oil. Season with additional salt and pepper, if needed.
7. Just before serving, add vinegar, tomatoes, and parsley and gently heat through. Rewarm pastrami hash. Serve warm soup topped with pastrami hash.