Preheat oven to 325°F (163°C). Heat olive oil in a Dutch oven over medium-high heat. Sear the short ribs on all sides until deeply browned, then remove and set aside.
Add onion, carrots, and celery to the pot. Cook until softened, then stir in garlic and tomato paste, cooking for another minute.
Pour in red wine and scrape up any browned bits from the bottom of the pot. Let it simmer for 5 minutes to reduce slightly.
Return the short ribs to the pot. Add beef broth, thyme, rosemary, and bay leaves. Cover and transfer to the oven.
Braise for 2.5 to 3 hours until the meat is fall-apart tender. Remove the ribs and strain the sauce if desired.
Serve the short ribs warm over mashed potatoes, buttered noodles, or polenta. Spoon sauce over the top.