Preheat the oven to 350°F (177°C). Generously grease a 9×13-inch baking pan. Set aside.

In a large bowl, whisk together the cake flour, baking powder, baking soda, and salt. Set aside.

In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter and sugar together on medium-high speed for 3 full minutes. Scrape down the sides and bottom of the bowl with a silicone spatula as needed. Beat in the eggs and vanilla extract until combined. Scrape down the sides and bottom of the bowl as needed. Beat in the sour cream.

Add half of the dry ingredients and half of the milk and beat on low speed until combined. Add the remaining dry ingredients and milk and beat on low speed until combined. Do not over-mix this batter. The batter will be smooth, velvety, and slightly thick. You may need to whisk it all by hand to make sure there are no lumps at the bottom of the bowl.

Spread the batter into the prepared pan and smooth it into an even layer. Bake for 32–38 minutes or until the top is very lightly browned and a toothpick inserted in the center comes out clean. Rotate the pan halfway through baking and, if you notice the top and edges quickly browning, tent the cake with aluminum foil.

Remove from the oven and allow the cake to cool in the pan placed on a wire rack. As the cake finishes cooling, make the frosting.

Using a handheld or stand mixer fitted with a paddle attachment, beat the butter on medium-high speed until pale, smooth, and creamy, about 3 minutes. Using a fine mesh strainer, sift the confectioners’ sugar and cocoa together. Add the sugar/cocoa mixture to the butter, then beat on low speed until the sugar is mostly incorporated, about 20 seconds. Stop the mixer, then add the milk, corn syrup, vanilla, and salt. Beat on medium-high speed for 2 minutes. If the frosting is too thick, beat in an extra splash of milk.

Spread the frosting over the cooled cake and top with sprinkles, if desired. Slice and serve.

Cover leftovers tightly and store in the refrigerator for up to 5 days.