Preheat the oven to 350°F (177°C). Line two 12-cup muffin pans with paper cupcake liners and set aside.

In the bowl of a stand mixer fitted with the paddle attachment, combine the cake flour, all-purpose flour, granulated sugar, baking powder, and kosher salt. Mix on low speed for approximately 1 minute until thoroughly combined.

With the mixer on low speed, add the butter a few cubes at a time, continuing until all butter has been added. Mix until the mixture resembles coarse sand.

Add the eggs one at a time, allowing each to fully incorporate before adding the next. Scrape down the sides of the bowl as necessary to ensure even mixing.

With the mixer running on low speed, gradually pour in the milk and vanilla extract. Once incorporated, increase the mixer speed to medium and beat for 2 minutes, scraping down the bowl as needed. The batter should be smooth and slightly thick.

Using a rubber spatula, gently fold in the rainbow sprinkles until evenly distributed throughout the batter.

Fill each cupcake liner approximately two-thirds full with batter (about ¼ cup). Bake in the preheated oven for 15 to 20 minutes, or until a toothpick inserted into the center of a cupcake comes out clean.

Allow the cupcakes to cool in the pan for 10 minutes. Then transfer them to a wire rack to cool completely before frosting.

In a clean stand mixer bowl fitted with the wire whisk attachment, beat the butter on medium-high speed for 5 minutes, pausing to scrape down the bowl once or twice. Reduce the speed to low and gradually add the powdered sugar. Once fully incorporated, add the vanilla extract. Increase the speed to medium-high and whip until light and fluffy, approximately 2 more minutes.

Once cupcakes are completely cooled, frost as desired. Garnish with additional sprinkles.