01 - Preheat the oven to 350°F. Grease a quarter sheet pan (9x13 inches) and line with parchment paper for easy removal.
02 - In a medium bowl, whisk together cake flour, baking powder, baking soda, and kosher salt until evenly blended.
03 - Using a stand mixer, beat unsalted butter, vegetable shortening, granulated sugar, and light brown sugar on medium-high speed until light and fluffy, approximately 2-3 minutes. Scrape down the bowl sides.
04 - Add eggs one at a time, beating thoroughly after each addition. Reduce mixer speed and pour in buttermilk, whole milk, and clear vanilla extract. Mix until fully incorporated.
05 - On low speed, gradually add the dry ingredients and mix just until combined. Gently fold in rainbow sprinkles by hand.
06 - Pour batter into the prepared pan and smooth the top. Bake for 28-32 minutes until a toothpick inserted in the center comes out clean. Cool completely in the pan.
07 - Lower oven temperature to 300°F. In a bowl, combine cake flour, granulated sugar, light brown sugar, baking powder, kosher salt, and rainbow sprinkles. Add melted butter and clear vanilla extract, mixing with a fork until small clusters form.
08 - Spread the crumb mixture on a parchment-lined baking sheet. Bake for 15 minutes, stirring halfway through cooking time. Cool completely.
09 - In a stand mixer, beat unsalted butter, vegetable shortening, and cream cheese until smooth. Add clear vanilla extract and kosher salt. Gradually beat in powdered sugar until fluffy. Add whole milk as needed to achieve spreadable consistency.
10 - In a small bowl, whisk together whole milk and clear vanilla extract until fully blended.
11 - Using a 6-inch cake ring, cut two full circles and two half circles from the cooled cake sheet.
12 - Place a cake round inside a lined 6-inch cake ring set on a cake board. Brush with vanilla soak mixture. Spread one-fifth of the frosting over the cake and sprinkle with one-third of the baked crumbs.
13 - Arrange half-circle pieces to fill gaps, brush with vanilla soak, spread frosting, and sprinkle crumbs. Repeat with remaining layers. Top with final cake round, apply soak, and finish with frosting and remaining crumbs.
14 - Refrigerate the assembled cake in the ring for at least 1 hour, or overnight. Remove the ring, transfer to a serving platter, and bring to room temperature before serving.