Preheat your oven to 325 degrees. Spray a 9×13 metal pan on the bottom, line with parchment paper, and spray again. If you need to use metal binder clips to hold down the sides, remember to use metal, not plastic. Set aside
In a medium size bowl whisk the flour, baking powder, and salt. Set aside.
In a bowl of a stand size mixer fitted with the paddle attachment, cream the butter, oil, sugar, and the pistachio pudding on medium-high until light and fluffy. Around 5 minutes.
With a rubber spatula scrape down the sides of the bowl, and start adding one egg at a time, beating on medium speed for 30 seconds between each addition. Make sure to also scrape the bottom of the bowl after each egg. Once they are all incorporated beat on medium speed for 1 minute. Add the vanilla and mix on low.
Add ⅓ of the flour mixture followed by half of the buttermilk. Mix just until combined and then add ⅓ of the flour mixture, followed by the rest of the buttermilk. Finish off with the rest of the flour mixture. Mix on low. With a rubber spatula, make sure to scrape the bottom of the bowl.
Evenly distribute the cake batter to the prepped sheet pan. With the back of a spoon, even out the batter to ensure it’s smooth for baking.
Bake for 40-45 minutes. Check the cake by inserting a toothpick. It’s done when it comes out with just a few moist crumbs on it.
Let it completely cool in the cake pan. While the cake cools, make the cream cheese buttercream.
For the cream cheese buttercream
In the bowl of an electric mixer, combine the butter and cream cheese. Beat on medium speed for about 2 minutes. Scrape down the sides and bottom of the bowl. Beat again for 2 more minutes.
With the mixer on low, add the powdered sugar, followed by the cream, vanilla extract, and a pinch of salt. Beat on low just until combined. With a rubber spatula, scrape down the sides of the bowl.
Turn the mixer up to medium-high speed and beat for about 3 to 5 minutes.
With a rubber spatula or a wooden spoon, beat out all of the air pockets by hand for a smooth look.
When the cake is cooled, use an offset spatula and frost the top of the cake. This cake is good served at room temperature or cold. However you serve it, it will not disappoint!