Pat the boneless short ribs dry and season generously with salt and pepper
Heat oil in a heavy pot or skillet over medium-high heat
Sear the short ribs on all sides until deeply browned
Remove the ribs and sauté chopped onion, carrot, and celery in the same pot
Add garlic and cook briefly
Stir in tomato paste and cook for 1 to 2 minutes
Deglaze with beef broth, red wine, or both
Add herbs such as thyme, rosemary, and bay leaf
Return the short ribs to the pot
Cover and braise in a 300°F oven or on low heat on the stovetop
Cook until fork-tender, about 2.5 to 3.5 hours
Check occasionally and add more liquid if needed
Remove the ribs and skim excess fat from the sauce
Reduce the sauce on the stovetop if desired
Serve the short ribs with the sauce over mashed potatoes, rice, or polenta