Pat the lamb shanks dry and sprinkle with salt and pepper.
Heat 2 tbsp of olive oil in a heavy based pot over high heat. Sear the lamb shanks in 2 batches until brown all over, about 5 minutes.
Remove lamb onto a plate and drain excess fat (if any) from the pot.
Turn the heat down to medium low. Heat remaining 1 tbsp of olive oil in the same pot, if needed. Add the onion and garlic, cook for 2 minutes.
Add carrot and celery. Cook for 5 minutes until onion is translucent and sweet.
Add the red wine, chicken stock, crushed tomato, tomato paste, thyme and bay leaves. Stir to combine.
Place the lamb shanks into the pot, squeezing them in to fit so they are mostly submerged.
Turn stove up, bring to a simmer. Cover, then transfer to the oven for 2 hours (see notes for other cook methods).
Remove from oven, remove lid, then return to the oven for another 30 minutes (so 2 1/2 hours in total). Check to ensure lamb meat is ultra tender (use 2 forks) – if not, cover and keep cooking. Ideal is tender meat but still just holding onto bone.
Remove lamb onto plate and keep warm. Pick out and discard bay leaves and thyme. Strain the sauce into a bowl, pressing to extract all sauce out of the veggies.
Pour strained sauce back into pot. Bring to simmer over medium heat and reduce slightly to a syrupy consistency. Taste then add salt and pepper to taste.
Serve the lamb shanks on mashed potato or cauliflower puree with plenty of sauce! Garnish with thyme leaves if desired.
OTHER COOK OPTIONS: *Slow cooker – Follow recipe to step 7. Bring sauce to simmer, scrape bottom of pot to get all brown bits into the liquid. Place shanks in slow cooker, add the sauce. Cook on low for 8 hours. Remove shanks, strain and reduce sauce to desired thickness on stove (or you could blitz, you won’t need to reduce).
*Pressure Cooker – Follow Slow Cooker steps, cook for 40 minutes on high. Release pressure according to manufacturer directions.
*Stove – to cook this on the stove, cook for about 2 hours on low, ensuring that you check it at 1 hour then every 30 minutes thereafter to ensure there is enough braising liquid (because liquid evaporates faster on the stove) and the bottom of the pot isn’t catching. Turn the lamb shanks twice. You won’t get the brown crust, but the flavour is the same!