Heat the olive oil in a large stock pot over medium heat.
Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for another minute until fragrant.
Add the diced carrots and celery to the pot and sauté for an additional 5 minutes, stirring occasionally.
Incorporate the shredded or diced prime rib into the pot, mixing well.
Pour in the beef broth and water, followed by the diced tomatoes.
Season the mixture with thyme, rosemary, bay leaf, salt, and pepper.
Bring the soup to a boil, then reduce the heat to low.
Add the chopped green beans and diced potatoes. Cover the pot and simmer for 30 minutes, or until the vegetables are tender.
If using, add the frozen corn during the last 10 minutes of cooking.
Taste and adjust seasoning, removing the bay leaf before serving.
Serve hot, garnished with fresh parsley if desired.