Preheat the oven to 175 ℃ 9350 ℉). Heat olive oil in a large pot or Dutch oven over medium-high heat.
Add the lamb shanks and sear them on all sides until they get a golden colour. This step adds flavour to both the meat and the sauce.
Once browned, take them out on a plate and set them aside.
In the same pot, lower the heat a bit. Add shallots and cook until they soften. Add garlic, carrots, and celery. Sauté for about 5 minutes.
Stir in rosemary, thyme, bay leaves, salt, and freshly ground pepper, sauté for a few seconds.
Place the lamb shanks back into the pot. Pour in the broth (or water) and bring everything to a boil.
Once it boils, cover the pot, place it to hot oven, and let it cook gently for about 2 to 2½ hours.
Check for seasoning at the end. If the sauce is too thin, you can uncover the pot and simmer for another 10–15 minutes to thicken it up a bit.