Pat the beef short ribs dry
Season all sides with salt and pepper
Heat oil in a heavy 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, carrot, and celery to the pot
Cook until softened
Add garlic and cook briefly
Stir in tomato paste and cook for 1 to 2 minutes
Deglaze with beef broth, wine, or both
Return the short ribs to the pot
Add herbs such as thyme, rosemary, or bay leaves
Cover and cook low and slow in the oven at 300°F to 325°F
Cook until the meat is very tender and falling off the bone
Skim excess fat from the sauce if needed
Serve hot with the cooking liquid or strained sauce