Bake cake according to directions in either two rounds, one 9×13 or one 1/2 sheet pan.  Allow to cool completely before filling and frosting.

While cake is baking, whisk together flour and milk in a small saucepan.  Cook over medium heat until thick and bubbly, whisking continually.  Allow this mixture to come to room temperature before adding to the next step.

In your stand mixer with the whisk attachment, beat together the butter and shortening until smooth.  Gradually add the sugar, then scrape down the sides of the bowl.  Beat on high for 15 minutes, stopping to scrape down the sides every five minutes.  Add the cooled milk mixture to the bowl and beat until combined completely.

Spread the cream filling between the layers of your cake, or over the top of the 9×13 cake.  Put cake in the fridge to help the cream filling firm up.

For chocolate  topping, mix together the egg and powdered sugar in a medium bowl.  Put butter and chocolate chips in a small microwave safe bowl and heat on high for one minute.  Stir together until smooth.  Add chocolate to the powdered sugar mixture and mix until smooth.  Add enough hot water to make the chocolate spreadable to frost your cake.  I store my cake in the fridge and take it out a little before serving.