In a large bowl, combine the flour, sugar, baking powder, and salt.
Add the butter, shortening, 2 Tbs milk and vanilla.
On low speed, blend together, about 30 seconds. Increase the speed to medium-high and continue beating for 2 minutes. Beat the egg with the remaining milk.
In 3 parts, beat the egg mixture into the flour mixture, about 20 seconds after each addition, until smooth.
Prepare springform pan and add batter. Bake at 350 until a tester inserted in the center comes out clean and the cake springs back when lightly touched, about 30 to 40 minutes.
Cool for 10 minutes, remove to wire rack and cool 1 hour.
cut the cake horizontally in half. Place a cake layer on a serving plate, spread with pastry cream, and top with the second cake layer.
Pour icing over top