Pat the lamb shanks dry and season generously with salt and pepper
Heat oil in a heavy pot or Dutch oven over medium-high heat
Sear the lamb shanks on all sides until deeply browned
Remove the shanks and set aside
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 red wine or stock, scraping up browned bits
Add beef or lamb stock, herbs, and any desired aromatics
Return the lamb shanks to the pot
Bring to a simmer
Cover and cook in a low oven at 325°F to 350°F or on low stovetop heat
Cook until the meat is very tender and falling off the bone
Turn the shanks occasionally during cooking
Remove the shanks from the pot
Simmer the cooking liquid to reduce if needed
Serve the lamb shanks with the sauce and desired sides