Preheat your oven to 160°C (320°F). Pat the lamb shanks dry with paper towels, then season generously with salt and pepper on all sides.
Heat a tablespoon of olive oil in a heavy Dutch oven over medium-high heat until shimmering. Carefully place the shanks in the pot, searing each side for about 4-5 minutes until deeply browned and fragrant. Use tongs to turn them, ensuring an even crust develops.
Remove the browned shanks and set aside. In the same pot, add chopped onions and carrots, cooking for about 5 minutes until they soften and release a sweet aroma. Stir occasionally with a wooden spoon, scraping up any browned bits from the bottom.
Add minced garlic to the vegetables and cook for 30 seconds until fragrant, filling the kitchen with a warm, pungent aroma. Pour in the red wine, scraping the bottom of the pot to loosen any flavorful browned bits, and bring to a simmer.
Let the wine simmer gently, reducing by half over about 10 minutes, until it turns a rich, glossy deep red. Return the lamb shanks to the pot, nesting them among the vegetables, then add the sprigs of rosemary and thyme.
Pour in enough broth to nearly cover the shanks, about 500ml. Bring the mixture to a gentle simmer, then cover the Dutch oven with its lid. Transfer the pot to the oven and braise for 2.5 to 3 hours, or until the meat is deeply flavorful, pulling away from the bone with a gentle tug.
Every 45 minutes, check the pot and add a splash more broth if the liquid reduces too much. Keep the simmer gentle to prevent the meat from becoming tough and allow the flavors to meld beautifully.
Once cooked, carefully remove the shanks and set aside to rest for about 10 minutes. Meanwhile, strain the sauce through a fine sieve into a saucepan, discarding the solids. Reduce the sauce over medium heat until it thickens slightly and becomes glossy.
Taste and adjust seasoning with salt and pepper. Serve the lamb shanks topped with the rich, wine-infused sauce, alongside crusty bread or hearty mash for a complete, comforting meal.
