Preheat the oven to 350 degrees F. Grease 3 8-inch cake pans with butter or spray. Then, line the bottom of each pan with parchment paper. Grease the parchment paper.
In a bowl, whisk together the flour, baking soda, cinnamon, and salt.
In a large bowl, cream together the sugar, oil, eggs, pineapple, and vanilla.
Add the dry ingredients to the wet and mix just until combined.
Add the carrots and pistachios and mix until combined.
Divide the batter evenly between the cake pans. Bake for 20 to 25 minutes or until the center is cooked through and a toothpick comes out clean. *See note below.
Allow the cakes to cool completely in the cake pans.
Make the Chai Buttercream and Frost the Cake
To the bowl of a stand mixer fitted with a paddle attachment, beat the butter and cream cheese together until combined.
Add the powdered sugar, spices, and vanilla extract and whip on medium-high until the buttercream is light and airy, about 5 minutes.
Place one layer of cake on a stand or plate. Spread buttercream evenly over the top. Then, repeat with the next layer of cake and frosting. And finally, the top layer of cake.
Apply a thin layer of frosting to the top and sides, smoothing it out as you work to create a crumb coat. Place the cake in the fridge for 30 minutes.
Finish frosting the cake with the rest of the buttercream, applying an even layer all over.
Optional: Decorate with extra chopped pistachios around the base of the cake.
Notes
*As the cakes bake, it's likely they won't all be done at exactly the same time. Remove each cake right as it's ready and allow the other cake(s) to finish baking.*After a day or so, the cake should be kept covered in the fridge for freshness.