Line the slow cooker pot with foil and apply a light coating of non-stick cooking spray.
In a medium-sized bowl, whisk together the dry ingredients including flour, baking powder, and kosher salt. Set aside.
In a large bowl, cream together the unsalted butter and shortening until a light and fluffy consistency is achieved. Incorporate the vanilla extract into the mixture, followed by the addition of the egg whites.
Gradually alternate between adding the flour mixture and the whole milk to the wet ingredients, starting and ending with the flour mixture. Begin by adding one-third of the flour mixture, then half of the whole milk, followed by another one-third of the flour mixture, the remaining milk, and finally the last one-third of the flour mixture. Mix the ingredients until just combined.
Gently fold in the rainbow sprinkles to distribute them evenly throughout the batter.
Pour the prepared batter into the lined slow cooker pot, ensuring an even distribution.
Place a paper towel atop the slow cooker pot and firmly cover it.
Activate the slow cooker on high heat for a duration of 2 hours, refraining from lifting the lid during this period.
After 2 hours, assess the cake's doneness by inserting a toothpick into its center. If the toothpick emerges clean, the cake is fully cooked. Allow the cake to cool within the slow cooker pot for approximately 15 minutes.
Carefully transfer the cake from the slow cooker pot to a wire rack to permit complete cooling.
While the cake cools, proceed with preparing the buttercream frosting. In a spacious mixing bowl, combine the unsalted butter and shortening, beating the mixture until it reaches a smooth consistency.
Incorporate 2 cups of powdered sugar into the mixture, continuing to mix until the frosting achieves a smooth texture.
Introduce the vanilla extract and 1 tablespoon of heavy cream, blending the ingredients thoroughly.
Gradually add the remaining 2 cups of powdered sugar, mixing until a smooth and creamy consistency is achieved.
Adjust the frosting's thickness by gradually incorporating additional heavy cream until the desired consistency is obtained. Add a pinch of kosher salt to taste.
Once the cake has completely cooled, apply a generous layer of the prepared vanilla buttercream frosting to its surface. Optionally, adorn the frosted cake with extra rainbow sprinkles.
Proceed to slice, serve, and enjoy this slow cooker birthday cake!