Preheat the oven to 350°F (180°C). Line a 9×13 inch baking pan with parchment paper.
In a medium bowl, whisk together the cake flour, baking powder, baking soda, and salt. Set aside.
In a stand mixer fitted with the paddle attachment or using a hand mixer, cream together the butter, coconut oil, and granulated sugar on medium-high speed for about 5 minutes until pale, light, and fluffy. Scrape down the bowl halfway through.
With the mixer running on low, slowly pour in the egg whites. Increase speed to medium and whip for 1-2 minutes until fully combined.
Add the vanilla bean paste, vanilla extract, imitation vanilla extract (if using), and almond extract (if using). Mix until fully incorporated.
Reduce mixer speed to low. Add 1/3 of the flour mixture, mixing just until combined. Pour in 1/2 of the buttermilk, mix briefly, then add the remaining flour and buttermilk alternately. Start and end with the dry ingredients. Mix until no dry pockets remain.
Pour the batter into the prepared pan and spread into an even layer. Bake for 30 minutes or until a toothpick inserted in the center comes out clean.
Remove from oven and let the cake cool completely in the pan.
For the icing: Beat the softened butter and cream cheese on medium-high speed for 2 minutes until completely smooth and fluffy.
Add the salt, almond extract, and vanilla. Mix on low until combined.
With the mixer on low, add the powdered sugar 1 cup at a time until fully incorporated. Once added, increase speed to medium-high and whip for 2 minutes until light and airy.
Assembly: Once the cake is completely cool, use a 3-inch round cutter to cut 8 rounds from the sheet cake. Press each round gently into individual ramekins.
Top each ramekin with 2 tablespoons of cream cheese icing, spreading evenly with a spatula.
Spread 1/4 cup of nonpareils onto a plate. Place each ramekin face-down onto the sprinkles, pressing lightly so the icing is fully coated. Serve immediately.