Start by patting the lamb shanks dry with paper towels. Season generously with salt and pepper on all sides. This step ensures a good sear and seals in the juices.
Heat the olive oil in your Dutch oven over medium-high heat. Once hot, add the lamb shanks and brown each side for about 4-5 minutes until they have a deep golden crust. Remove the shanks and set aside.
In the same pot, add the chopped onion, diced carrots, and celery. Cook for 5-7 minutes, stirring occasionally, until the vegetables soften and begin to caramelize. Add the minced garlic and sauté for another minute until fragrant.
Add the tomato paste and stir into the vegetables. Pour in the beef broth and diced tomatoes, scraping the bottom of the pot with your wooden spoon to release all the browned bits. These bits are packed with flavor!
Stir in the chopped rosemary and thyme. Return the lamb shanks to the pot, nestling them into the liquid and vegetables. The liquid should come about halfway up the shanks.
Bring the liquid to a gentle simmer. Cover the pot with a tight-fitting lid and transfer to a preheated oven at 325°F (160°C). Let the lamb cook for 2.5 to 3 hours until the meat is incredibly tender and easily pulls away from the bone.
Carefully remove the lamb shanks from the pot. If desired, reduce the sauce on the stove over medium heat for 5-10 minutes to thicken. Serve the lamb topped with the rich sauce alongside your favorite sides, such as Cheesy Scalloped Potatoes Gratin or a crisp green salad.
