Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 10x15 inch pan. Line a second 10x15 inch pan with parchment paper.
In a large bowl, combine cake mix, pudding mix, 1/4 cup oil, 1 1/2 cup milk and 4 eggs. Beat 4 minutes on high speed. Divide batter into the two 10x15 inch pans.
Bake in preheated oven for 12 to 15 minutes, or until a toothpick inserted into cake comes out clean. Allow to cool.
To make the filling: In a large bowl, combine 2 cups confectioners' sugar, 1/2 cup milk, shortening, butter, vanilla and flour. Beat on high speed for 5 minutes, or until it achieves the consistency of whipped cream.
Spread filling over the layer in the greased pan. Loosen the sides of the other layer by running a knife around the edge between the cake and the pan. Flip the cake onto the frosted layer.
Remove the pan and parchment paper from the top layer and serve.
