Pat the lamb shanks dry with paper towels, then season generously with salt and pepper on all sides. Set aside.
Heat olive oil in a Dutch oven over medium-high heat until shimmering. Carefully place the shanks in the pot, searing each side for about 4-5 minutes until they develop a deep, golden-brown crust. Use tongs to turn and ensure even browning. Transfer the browned shanks to a plate and set aside.
Add chopped onion and minced garlic to the same pot. Cook over medium heat, stirring occasionally, until the onion is translucent and fragrant, about 5 minutes. You should see the bits from searing loosen and start to soften.
Stir in the tomato paste, cooking for about 1 minute to deepen the flavor. Pour in the red wine, scraping up any browned bits from the bottom of the pot with a wooden spoon. Bring the mixture to a gentle boil and let it reduce by half, about 8 minutes, until it thickens slightly and releases a rich aroma.
Return the seared lamb shanks to the pot, nestling them into the wine mixture. Add fresh thyme and rosemary, then pour in enough broth to partly submerge the meat, about 2 cups. Bring everything to a gentle simmer.
Cover the pot with a tight-fitting lid and transfer it to a preheated oven at 160°C (320°F). Let the shanks braise slowly for about 2.5 to 3 hours, checking once or twice to ensure the liquid stays at a gentle simmer. The meat should become tender and easily pull apart.
Once cooked, carefully remove the lamb shanks from the pot and set aside. Place the pot back on the stove over medium heat and simmer the sauce uncovered for about 10 minutes, stirring occasionally, to thicken it into a glossy, flavorful glaze.
Taste the sauce and adjust the seasoning with more salt and pepper if needed. Serve the lamb shanks hot, spooning the rich sauce over the meat, and garnish with fresh herbs if desired. Enjoy the melt-in-your-mouth tenderness paired with the deep wine sauce.
