Preheat oven to 325°F (160°C). Season short ribs with salt and pepper.
Heat olive oil in a large Dutch oven or oven-safe pot over medium-high heat. Sear short ribs in batches until browned on all sides. Remove and set aside.
Add onion, celery, and carrots to the pot and cook until softened, about 5-7 minutes. Add garlic and cook for 1 minute more.
Pour in red wine and scrape up any browned bits from the bottom of the pot. Cook for 2 minutes.
Stir in tomato paste, thyme, and rosemary. Cook for 1 minute.
Return short ribs to the pot. Pour in beef broth until the ribs are mostly covered. Bring to a simmer.
Cover the pot and transfer to the preheated oven. Braise for 3-4 hours, or until the short ribs are fork-tender.
Remove the short ribs from the pot and let rest. Skim off any excess fat from the sauce.
Serve the short ribs with the sauce, garnished with fresh herbs if desired.
Notes
Serve with creamy polenta, mashed potatoes, or egg noodles.