Preheat oven to 375°.
In a large sauté pan, heat oil. While oil is heating up, salt and pepper all sides of short ribs.
Place ribs in sauté pan and brown all sides. Remove and place in heavy dutch oven.
Cut celery and tri-colored carrots into 2 inch pieces and place around ribs.
In sauté pan, add 1 medium onion (diced into small pieces) and cook until translucent, about 5-8 minutes.
Add red wine, tomato paste, rosemary and beef base and cook for 1 minute and then add mixture to short ribs.
Peel chippolini onions and add to ribs.
Cover and place in oven and cook for 30 minutes.
Reduce heat to 325° and continue to cook for 1 hour 30 minutes (or until beef is tender).
Remove from oven. Serve over mashed potatoes, spooning liquid mixture and vegetables on top.