Preheat the oven to 325°F
Pat beef short ribs dry
Season with salt and black pepper
Heat oil in a large oven-safe pot or Dutch oven
Sear the short ribs on all sides until browned
Remove the short ribs from the pot
Add chopped onion, carrots, and celery to the pot
Cook until softened
Add minced garlic and cook briefly
Stir in tomato paste
Add red wine or beef broth
Scrape up browned bits from the bottom of the pot
Add beef broth, bay leaves, thyme, and rosemary
Return the short ribs to the pot
Cover and bring to a simmer
Transfer to the oven
Braise for 2.5 to 3.5 hours until tender
Remove the short ribs from the pot
Skim excess fat from the sauce
Simmer the sauce to thicken if needed
Serve the short ribs with the sauce
Garnish with chopped parsley if desired