Bring the stock to a boil in a large saucepan, stir in the rice, cover, reduce the heat and simmer for 20 to 25 minutes, until the rice is tender.

In a large bowl, combine the yogurt, flour and egg yolks, mixing with a wooden spoon until smooth. Add the cold water in a thin stream while stirring constantly. Stir yogurt mixture into the hot soup, season with salt and pepper, cover and gently simmer for 10 minutes.

Heat butter in a small saucepan until foamy. Add the dried mint and leave on low heat for 1 minute. Pour warm butter mixture over the soup, and serve immediately. (If soup is to be reheated later for another serving, thin it with water).