Heat 3 tablespoons peanut oil in a large heavy skillet over medium-high heat.
Brown the lamb shanks well on all sides.
When brown, transfer shanks to a large stock pot.
Cover them with water.
Add the onion, carrot, bay leaves, cloves, and peppercorns.
Bring to a boil, then lower heat and simmer shanks 30 to 45 minutes until done.
While shanks are simmering, prepare the yogurt sauce.
Mix the yogurt, egg yolks, cornstarch, and salt together in a large enameled or stainless-steel pan.
Gently boil the sauce for 10 minutes, stirring constantly to prevent lumping and scorching.
Keep warm.
When ready to serve, fry the garlic and mint in remaining 1/2 cup oil over medium-high heat, stirring well, until garlic browns and mint turns crisp.
Place the braised lamb shanks on a large serving platter.
Coat with hot yogurt sauce, top with crisp garlic and mint mixture.