01 - Preheat oven to 350°F. Grease a quarter sheet pan (9x13 inch) and line with parchment paper.
02 - Whisk together cake flour, baking powder, baking soda, and salt in a medium bowl.
03 - Using a stand mixer, beat butter, shortening, granulated sugar, and brown sugar on medium-high speed until light and fluffy, 2–3 minutes. Scrape down bowl sides.
04 - Add eggs one at a time, beating well after each addition until fully incorporated.
05 - Reduce mixer speed to low. Add buttermilk, whole milk, and vanilla extract; mix until combined. Gradually add dry ingredients and mix just until incorporated. Fold in rainbow sprinkles.
06 - Pour batter into prepared pan and smooth top. Bake for 28–32 minutes until a toothpick inserted in center comes out clean. Cool completely in pan.
07 - Lower oven temperature to 300°F. In a bowl, combine cake flour, granulated sugar, brown sugar, baking powder, salt, and sprinkles. Add melted butter and vanilla; mix with fork until small clusters form.
08 - Spread crumb mixture on a lined baking sheet. Bake for 15 minutes, stirring halfway through. Cool completely.
09 - Beat butter, shortening, and cream cheese in stand mixer until smooth. Add vanilla and salt. Gradually beat in powdered sugar until fluffy. Add milk, 1 tablespoon at a time, until spreadable consistency is reached.
10 - Whisk together whole milk and vanilla extract in a small bowl.
11 - Using a 6-inch cake ring, cut two full circles and two half circles from the cooled cake sheet.
12 - Place a full cake round inside a lined 6-inch cake ring set on a cake board. Brush with vanilla soak. Spread 1/5 of frosting over cake, then sprinkle 1/3 of crumbs.
13 - Add half-circles to fill gaps. Brush with vanilla soak, spread frosting, and sprinkle crumbs. Repeat with remaining cake round. Top with final soak, frosting layer, and remaining crumbs.
14 - Refrigerate cake in ring for at least 1 hour or overnight. Remove ring and transfer to serving platter. Serve at room temperature.