Preheat the oven to 300°F
Pat the beef short ribs dry
Season all sides with salt and black pepper
Heat oil in a large oven-safe pot or Dutch oven over medium-high heat
Sear the short ribs on all sides until browned
Remove the ribs from the pot
Add chopped onion, carrots, and celery to the pot
Cook until softened
Add garlic and cook briefly
Stir in tomato paste
Add beef broth, red wine, or both
Add thyme, rosemary, and bay leaves
Return the short ribs to the pot
Cover with a lid
Place in the oven
Bake for 2.5 to 3.5 hours
Cook until the meat is very tender and pulls away easily
Remove from the oven
Skim excess fat if needed
Serve hot with the cooking liquid or strained sauce