Preheat your oven to 160°C (320°F). Season the lamb shanks generously with salt and pepper.
Heat a tablespoon of olive oil in your Dutch oven over medium-high heat until shimmering. Place the shanks in the pot and sear until deeply golden brown, about 4-5 minutes per side, until a rich crust forms and you can smell that nutty aroma.
Transfer the seared shanks to a plate. In the same pot, add chopped onions and carrots, cooking over medium heat until softened and fragrant, about 8 minutes. Stir occasionally to release their sweet aroma and scrape up any browned bits.
Add minced garlic to the vegetables and cook for another minute until fragrant, filling your kitchen with a warm, savory smell.
Pour in the red wine and bring to a gentle simmer, scraping the bottom of the pot to loosen browned bits. Let it reduce by half, about 10 minutes, until the wine turns glossy and fragrant.
Return the lamb shanks to the pot, placing them on top of the vegetables. Add sprigs of rosemary and thyme, then pour in the stock to come halfway up the meat. Bring to a gentle simmer.
Cover the pot with a lid and transfer to the oven. Braise for 2.5 to 3 hours, checking occasionally to ensure the liquid covers the meat. The meat should become fall-apart tender and the sauce deep and glossy.
Once cooked, carefully remove the shanks and set aside. Place the pot back on the stove over low heat and simmer the sauce until thickened and aromatic, about 10-15 minutes. Adjust seasoning with salt and pepper if needed.
Return the lamb shanks to the sauce, letting them soak up all the rich flavors for a few minutes. Then, serve hot, spooning the glossy sauce over each shank, garnished with fresh herbs if desired.