Oven method:

1. Preheat the oven to 180°C (350°F) (160°C/325°F fan-forced). 
2. Heat 2 tablespoons of the olive oil in a heavy-based ovenproof frying pan over medium–high heat.
3. Sprinkle the lamb shanks with salt, then sear on all sides for 3–5 minutes. Set aside.
4. Add the remaining 1 tablespoon of olive oil to the same pan (if your pan is very sticky, see note 2).
5. Add the onion, garlic, carrot and celery and cook for 3–4 minutes until softened. Stir in the tomato paste.
6. Return the lamb shanks to the pan, along with the red wine. Cook for 5 minutes until the red wine has reduced by half, scraping up any caramelised bits on the bottom of the pan.
7. Add the chicken stock and thyme to the pan, place the lid on (or cover tightly with two layers of foil) and bake for 2½ hours. The meat should fall off the bone easily. If not, continue cooking in 20-minute intervals until it is tender. Remove the thyme sprigs before serving.
8. Serve with mashed potatoes and steamed peas.

Slow-cooker method:

1. Sear first for flavour (optional but recommended) – Heat the olive oil in a pan, season and brown the lamb shanks on all sides for 3–5 minutes. Remove and set aside on a plate. To the same pan, add the onion, garlic, carrot and celery. Cook for 3–4 minutes until softened, then stir in the tomato paste. Deglaze with the red wine and cook until reduced by half. (If you’re short on time, you can skip the searing step and just add everything straight into the slow-cooker, but the flavour will be deeper if you take 10 minutes to sear/reduce.)
2. Transfer to the slow-cooker – Place the lamb shanks in the slow-cooker. Pour over the reduced wine mixture, then add the chicken stock and thyme.
3. Cook – Cover and cook on Low for 7–8 hours or High for 4–5 hours, until the lamb is tender and falling off the bone.
4. Finish the sauce – If the sauce looks thin at the end, remove the shanks and reduce the sauce in a saucepan on the stove for 10–15 minutes until rich and glossy. Alternatively, stir through a cornflour slurry (1 tablespoon of cornflour/cornstarch + 2 tablespoons of water) and simmer on High in the slow-cooker for 15 minutes.
5. Serve – As for the oven method, serve with creamy mashed potatoes and peas.