Step 1The night before you plan to serve this dish, drain the yogurt: Dampen a piece of cheesecloth and place it in a strainer. Place the strainer over a bowl and place the yogurt in the strainer. Cover and refrigerate for several hours or overnight. Discard liquid. You'll have one-half cup drained yogurt.
Step 2Heat 2 tablespoons oil in a large skillet. Add the onion and cook over high heat until reddish brown, about 5 minutes. Add the lamb and fry until brown, about 5 minutes. Add the tomato juice or water and salt and pepper to taste, and simmer over low heat for about 10 minutes.
Step 3Trim the leeks, then slice them lengthwise and wash thoroughly. Discard the tough green parts and chop the rest.
Step 4When the lamb is done, cut the nan into 4-inch triangles or squares. In a separate pan, heat 1 tablespoon oil and fry the bread until lightly browned but not too crisp. Remove the bread and keep warm. Add the leeks and the remaining 1 tablespoon oil to the pan and fry until the leeks are soft, about 3 to 4 minutes. Season to taste with salt and pepper.
Step 5To serve, cover the bottom of a large warmed dish with one-fourth cup drained yogurt, then add most of the bread, then the leeks. Place dollops of the remaining yogurt over the leeks, then add the meat. Sprinkle with red pepper and mint and garnish with the remaining fried nan.