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

Stir in the tomato paste and cook for another 2 minutes.

Pour in the red wine and beef broth, scraping up any browned bits from the bottom of the pot.

Add the rosemary and thyme. Bring to a simmer.

Return the lamb shanks to the pot, cover, and transfer to the oven. Braise for 2-2.5 hours, or until the meat is tender and falls off the bone.

Check occasionally and add more broth if necessary to keep the shanks partially submerged.

Remove the pot from the oven. Let the lamb shanks rest for a few minutes before serving.

Serve with the gravy spooned over the top, alongside mashed potatoes or polenta.