With your electric mixer, cream butter and shortening until combined.
Slowly add the powdered sugar and beat until light and fluffy. This is usually about 2 minutes.
Add vanilla, and mix to combine.
Leave at room temperature and add a thick layer to the top of your cake once the cake is completely cooled. It is okay if you get a little crumb in your cream layer, no one is gonna notice.
Place cake in refrigerator.
In mixing bowl cream together butter and cocoa, add vanilla and 2 cups powdered sugar, 1/3 cup cream and mix together.
Continue to add 2 cups powdered sugar and 1/3 cup cream on top of it and cream together. Adding the cream on top of the powdered sugar will help prevent it from flying all over your kitchen. Add a little water or more cream at the end to reach your preferred consistency. Your icing should be thick but smooth, creamy and easy to spread.
Remove cake from the refrigerator and spread the icing over the cream layer.
Return cake to the refrigerator to set for about an hour.