Preheat the oven to 300°F (150°C). In a large oven-safe pot or Dutch oven, heat the olive oil over medium-high heat. Season the lamb shanks with salt and black pepper. Sear the lamb shanks on all sides until browned, about 3-4 minutes per side. Remove from the pot and set aside.

In the same pot, add the chopped onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables are softened. Add the minced garlic and black garlic, and sauté for another minute until fragrant. Stir in the tomato paste and cook for an additional 2 minutes.

Pour in the red wine, scraping up any browned bits from the bottom of the pot. Allow the wine to cook down for about 5 minutes. Add the broth, rosemary, and thyme, and stir to combine.

Return the seared lamb shanks to the pot, ensuring they are submerged in the liquid. Bring to a simmer, cover the pot, and transfer it to the preheated oven. Roast for 2.5 to 3 hours, or until the lamb is tender and easily pulls away from the bone.

About 20 minutes before the lamb is done, prepare the couscous. In a separate pot, bring 1.5 cups of water to a boil. Stir in the couscous and mixed vegetables, cover, and remove from heat. Let it sit for 5 minutes, then fluff with a fork.

In a small bowl, combine the plain yogurt, chopped mint, lemon juice, and a pinch of salt. Mix well and set aside.

Once the lamb shanks are done, remove them from the oven and let them rest for a few minutes. Serve the lamb shanks over a bed of savory vegetable couscous, drizzling with some of the braising liquid. Top with a generous dollop of mint yogurt sauce.