1. Preheat oven to 350°F. Butter and flour two 9 inch round layer pans. Combine chopped cooked beets and applesauce in a blender and blend until smooth.

2. In a large mixing bowl in an electric mixer, cream together butter and sugar. Add eggs, one at a time, beating after each addition. Add vanilla, and then add the beet mixture, mixing well. Add the vinegar and the yogurt and mix well again.

3. In a separate bowl, mix the cocoa or chocolate powder, baking soda, flour, and salt together. Add to the wet ingredients and mix until well blended.

4. Pour batter into prepared pans and bake for approximately 30-35 minutes, or until a toothpick inserted in the center comes out clean. Cool in pans on a wire rack for 5 minutes before removing from pans and allowing to cool completely. When the cakes are cool, you may frost them.

Bring flour and water to a boil, reduce heat, and stir constantly until thick and slightly clear. Cool in the refrigerator for several hours or overnight. Cream together butter, sugar, and vanilla. Add the flour mixture and continue to beat until fluffy. Keep the frosting refrigerated before use.