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 cups milk and 4 eggs; beat 4 minutes on high speed on mixer.
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 icing sugar, 1/2 cup milk, shortening, butter, vanilla and flour; beat with mixer 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.