Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch baking pan.
In a medium bowl, stir together the cake mix and instant pudding. Add eggs, oil and water, mix until smooth. Pour into the prepared pan.
Bake for 30 to 35 minutes in the preheated oven, set aside to cool. Prepare filling using the second set of ingredients.
In a small saucepan, stir together the flour and milk, and cook over medium heat until boiling. Stir over heat until thick, about 2 minutes. Remove from heat and set aside to cool. In a medium bowl, cream butter, shortening, sugar and vanilla until light and fluffy. Gradually beat in the flour mixture at high speed. Invert cooled cake onto a tray. Split into two layers horizontally, and fill with the frosting. Replace top layer and cut into 3x2 inch rectangles. These keep better if individually wrapped.
