Pat the beef shank dry and season it with salt and pepper
Heat oil in a heavy pot over medium-high heat
Sear the beef shank on all sides until browned
Remove the beef shank from the pot
Add chopped onions, carrots, and celery to the pot
Cook until the vegetables soften
Add garlic and cook briefly
Stir in tomato paste if desired
Deglaze the pot with broth, wine, or water
Return the beef shank to the pot
Add enough liquid to come partway up the meat
Add herbs such as bay leaf, thyme, or rosemary
Bring to a simmer
Cover the pot with a lid
Cook on low heat until the meat is tender
Braise in the oven at 300°F to 325°F if preferred
Cook for several hours until the meat pulls easily from the bone
Check occasionally and add more liquid if needed
Remove the beef shank from the pot
Serve with the cooking liquid or strain and reduce it into a sauce