Pat the short ribs dry and season with salt and pepper.
Coat a large, nonstick pan with olive oil.
Sauté short rib pieces, over medium-high heat, for about 2 - 3 minutes on each side until browned. When finished, transfer the short ribs to a bowl. Do not remove pan. Lower heat to medium.
Add the onions to the pan. Cook over medium heat for about 3 minutes. When onions are translucent, add garlic. Cook for 1 minute.
Add Chianti, rosemary, beef broth and tomatoes to the pan one at a time, allowing the liquid to evaporate partially before each addition, about two minutes.
Reduce heat to medium low.
Return short ribs to the pan, including any juices that might have accumulated in the bowl.
Cover and let simmer for 3 hours on low heat to complete the braising process.
Remove the short ribs from the pan and boil the liquid until it’s reduced by half, about 10 minutes.
Return the short ribs to the pan and heat thoroughly.
Serve with potatoes or risotto and vegetables.