Heat the olive oil in a large soup pot over medium heat. Add the chopped onion, carrots, and celery. Sauté until the vegetables soften, about 5 to 7 minutes.
Stir in the minced garlic and cook for 1 minute. Pour in the beef broth, add the bay leaves and diced potato, and bring the mixture to a boil.
Add the corned beef and chopped cabbage, then continue simmering until the cabbage is tender and the meat is warmed through, about 20 minutes. If needed, add more broth to the soup.
Taste the soup and season with salt and pepper as needed. Serve hot, garnished with fresh parsley.