Preheat the oven to 325°F (160°C). Season the lamb shanks with salt and pepper.

In a Dutch oven, heat olive oil over medium-high heat. Sear the lamb shanks on all sides until browned, about 8-10 minutes. Remove and set aside.

In the same pot, add onion, celery, carrots, and garlic. Sauté until softened, about 5-7 minutes.

Pour in the red wine, scraping up any browned bits from the bottom of the pot. Bring to a simmer and reduce by half.

Add the beef broth, tomato paste, rosemary, thyme, and bay leaf. Return the lamb shanks to the pot.

Cover and transfer to the oven. Braise for 2 to 2.5 hours, or until the lamb is tender and falling off the bone.

Remove the lamb shanks from the pot and let rest for a few minutes. Skim excess fat from the sauce, then serve the shanks with the sauce spooned over the top.