Preheat your oven to 180°C (350°F).
Heat the olive oil in a large, heavy-based Dutch oven over medium-high heat. Add the lamb shanks and brown them on all sides. Once browned, remove the shanks from the pot and set them aside.
In the same pot, add the finely diced onion, diced celery, and chopped carrots. Sauté the vegetables over medium heat until they become soft and the onion is translucent, about 5-7 minutes. Add the chopped garlic and cook for another 1-2 minutes until fragrant.
Stir in the thyme, tomato paste, diced tomatoes, chicken stock, and red wine. Mix well to combine all the flavours.
Place the browned lamb shanks back into the pot, making sure they're submerged in the sauce. Cover the Dutch oven with a lid and transfer it to the preheated oven. Let the lamb shanks braise in the oven for 2 to 3 hours, or until the meat is tender and falling off the bone.
After 2-3 hours, remove the lid from the pot. Continue cooking the lamb shanks in the oven, uncovered, for an additional 30 minutes. This will help thicken the sauce and brown the lamb on top.
Once done, remove the lamb shanks from the oven and serve with the rich sauce spooned over mashed potatoes or your preferred side dish.