In a Dutch oven or large pot, cover rib bones, onion, celery and carrot with about 10 cups water. Bring to a boil, then allow to simmer over low heat for about 3 hours. Strain broth, skimming any fat (chilling the stock makes it easier to separate the fat from the broth). Store in air tight containers in the refrigerator or freezer. Reserve meat for soup. This can be done the day before you plan to make the soup.
Make the Prime Rib Beef and Lentil Soup:
In a Dutch oven or soup pot, heat olive oil over medium-low heat. Sauté onions until transparent, about 3 minutes. Stir in the garlic, celery and carrots, season with salt and pepper, and cook for about 5 minutes more. Add lentils and beef stock, and bring to boil. Lower the heat to a simmer, then cover the pot, and allow to cook, stirring periodically, for about 15 minutes. Stir in the meat from beef ribs, and simmer for another 15-20 minutes, partially uncovered, or until the lentils are fully cooked and tender. Stir in balsamic vinegar and adjust seasoning with salt and pepper if necessary. Serve hot with crusty bread.
If you didn't make prime rib but still want to make this delicious soup, then don't worry. Use store bought beef broth in place of the prime rib beef stock. For the meat, use any leftover roast beef or steak - leftover roasted tri-tip would work nicely here, too.