Cut meat into 4 serving pieces. Season with salt and pepper to taste. Dot with 1/4 cup butter and bake at 350 degrees, basting now and then with pan juices, about 40 minutes, or until well browned.
Stir rice into pan juices. Remove baking pan from oven and set aside while preparing yogurt sauce.
Combine yogurt with salt and pepper to taste. Stir in eggs until smooth. Set aside.
Melt remaining 1/2 cup butter and add flour. Saute until smooth. Add yogurt mixture and stir until smooth. Pour yogurt sauce in baking pan, stirring it with meat pieces, and bake at 375 degrees 45 minutes. Serve hot.