Preheat the oven to 350°F. Line three 6-inch cake pans with parchment paper.
To make the batter: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, and vanilla extract. Mix on low until combined and there are no chunks of butter. Add the milk, sour cream, applesauce, and whipping cream and mix to combine.
In a separate bowl, add the cake flour, cocoa, baking powder, and sea salt and whisk together. Add into the stand mixer with the butter.
Mix until a smooth batter forms, making sure to scrape down the sides of the bowl party way through mixing to ensure you have a smooth cake batter.
Divide the batter evenly into each cake pan, about 9.3 ounces each.
Bake for 20 to 22 minutes, until a toothpick inserted in the center comes out clean. Allow to cool completely in the cake pans. (If you're baking at high altitude, be sure to check the Notes at the bottom of the recipe for high altitude baking instructions).
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, shortening, cream cheese, powdered sugar, and milk. Mix on low until combined, then speed up the mixer to high for 1 minute, or until light and fluffy. Add in the sprinkles and mix on low until combined. Scrape the sides of the bowl and mix again to ensure sprinkles throughout. Transfer the batter to a piping bag with Ateco tip #827.
Place the first cake layer on your cake stand or plate. Starting on the outer edge of the cake, spiral the frosting around the boarder and then into the middle. Top with the second cake layer, repeat the process, top with the third layer, and repeat again.