Preheat the oven to 350°F.

Cut the lamb shoulder into four pieces, removing any excess fat and bones.

Season the meat with salt and pepper on both sides and place in a cast iron oven proof pan. Place butter cubes on the pieces of lamb. Bake in the oven, baste with the pan juices every ten minutes and bake for 40 minutes, or until well browned. Remove from the oven, stir the rice into the pan juices and set aside.

In a large bowl combine the yogurt with salt and pepper to taste. Break the five eggs into another bowl and beat lightly with a fork. Add the beaten eggs into the yogurt mixture and whisk until smooth. Set aside.

In a small skillet over medium heat, melt the 4 tablespoons of butter. Add the flour and whisk until all the flour is incorporated.

Add the flour mixture to the yogurt and whisk until smooth.

Pour the yogurt sauce over the lamb and bake for about 45 minutes, until the topping is set and the center of the casserole reaches 165°F (74°C). Check that the lamb and rice are tender; allow more time if needed. Remove from the oven, sprinkle with minced mint if using, and serve hot.