Season the lamb shanks generously with salt and pepper.
In a large ovenproof pot, heat 1 tablespoon of olive oil.
Add the lamb shanks to the pot until they are well-browned on both sides. Then, remove the shanks from the pan and set them aside.
In the same pot, heat the rest of the olive oil and fry the onion, carrot, and garlic for about 8 minutes, until soft.
Add the rosemary sprigs and tomato paste and cook for 30 seconds before adding the red wine and stock.
Allow the contents of the pot to come to a simmer, then add the lamb shanks back into the sauce.
Cover the pot with a lid and place it in the oven to slowly braise for 3 hours until the lamb is soft and tender. Check the shanks halfway through the cooking time and add more broth if needed.
Remove the lid for the last 30 minutes of cooking to allow the sauce to thicken a little more.