Preheat your oven to 325°F (160°C).
Season the lamb shanks generously with salt and black pepper.
In a large, oven-safe pot or Dutch oven, heat olive oil over medium-high heat. Sear the lamb shanks until browned on all sides (about 8 minutes). Remove and set aside.
In the same pot, add the chopped onion, garlic, carrots, and celery. Cook for 5-7 minutes until softened.
Stir in the tomato paste and cook for 2 minutes to enhance the flavor.
Pour in the stout beer, scraping the bottom of the pot to deglaze. Let it simmer for 3-4 minutes.
Add the broth, rosemary, thyme, bay leaves, and Worcestershire sauce. Return the lamb shanks to the pot.
Cover the pot and transfer it to the preheated oven. Braise for 2 1/2 to 3 hours until the lamb is tender and falls off the bone.
Remove the lamb shanks and strain the sauce if desired. Simmer the sauce on the stovetop for 5-10 minutes to thicken if needed.
Serve the lamb shanks with the sauce, alongside mashed potatoes or crusty bread.