01 - Preheat the oven to 350°F. Grease and line a quarter sheet pan (9x13 inch) with parchment paper.
02 - In a bowl, whisk together cake flour, baking powder, baking soda, and salt until well combined.
03 - In a stand mixer, beat butter, shortening, and sugars on medium-high speed until light and fluffy, about 2-3 minutes. Scrape down the bowl.
04 - Add eggs one at a time, beating well after each addition. Reduce speed and add buttermilk, milk, and vanilla extract. Mix until combined.
05 - On low speed, add dry ingredients and mix just until incorporated. Gently fold in rainbow sprinkles.
06 - Pour batter into prepared pan and smooth the top. Bake for 28-32 minutes, until a toothpick inserted into the center comes out clean. Cool completely in the pan.
07 - Lower oven temperature to 300°F. In a bowl, combine flour, sugars, baking powder, salt, and sprinkles. Add melted butter and vanilla; mix with a fork until small clusters form.
08 - Spread crumb mixture on a lined baking sheet and bake for 15 minutes, stirring halfway through. Cool completely.
09 - In a stand mixer, beat butter, shortening, and cream cheese until smooth. Add vanilla and salt. Gradually beat in powdered sugar until fluffy. Add milk as needed for spreadable consistency.
10 - Mix whole milk and vanilla extract in a small bowl until combined.
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 milk soak. Spread 1/5 of frosting over the cake and sprinkle 1/3 of the crumbs. Repeat layering with half-circles, milk soak, frosting, and crumbs.
13 - Top with final cake round, soak, and finish with remaining frosting and crumbs. Chill cake in the ring for at least 1 hour or up to overnight. Remove ring and serve at room temperature.