Step 1

Make the cake: Position the rack in the middle of the oven and preheat to 350 degrees. Grease a 9-by-13-by-2-inch baking pan with softened butter. Line the pan with parchment paper.

Step 2

Using a sifter or fine-mesh strainer, sift the cake flour, all-purpose flour and baking powder into a large bowl; add the salt and whisk briefly to combine.

Step 3

Place the 3/4 cup of butter in a stand mixer fitted with the paddle attachment and beat it on medium speed until smooth and lightened in color, about 2 minutes. Add the sugar, oil and vanilla, and beat on medium until light and fluffy, about 5 minutes, scraping down the bowl with a rubber spatula as needed.

Step 4

Reduce the speed to low and add the eggs, one at a time, and then the yolks, also one at a time, stopping the mixer to scrape the bowl as needed.

Step 5

Add the dry ingredients in 3 additions, alternating with the ice water, beginning and ending with the dry, and scraping as needed.

Step 6

Transfer the batter to the prepared pan and bake for 30 to 35 minutes, rotating halfway through, until a cake tester comes out with a moist crumb or two, the cake bounces back when lightly pressed with your finger, and is just starting to come away from the sides of the pan.

Step 7

Transfer the cake to a wire rack and let cool to room temperature; then run a butter knife around the edges of the cake. Flip the cake out of the pan and onto the rack, peel off and discard the parchment paper, and then invert the cake right side up onto a rectangular serving plate.

Step 8

Make the frosting: Place the butter in the clean bowl of a stand mixer fitted with the paddle attachment and beat on low until smooth, about 3 minutes.

Step 9

Slowly add the confectioners’ sugar, 1 cup (119 grams) at a time. Once about a third of the sugar (about 2 1/3 cups/277 grams) is incorporated, stop the mixer and scrape the bowl with a rubber spatula. Add about a third of the heavy cream and mix until incorporated.

Step 10

Continue alternating sugar and heavy cream in this fashion, scraping with a spatula periodically, and taking time to let the mixer run in between the additions, until all the sugar and cream have been incorporated.

Step 11

Add the vanilla, vinegar and salt, increase the mixer speed to medium and continue to mix until quite light and fluffy, at least 5 to 10 minutes, if not longer. Add the food coloring halfway through the mixing time, if using.

Step 12

Generously frost the cooled cake with the frosting, making decorative swirls with the back of a spoon or offset spatula and sprinkling with the pink sparkling sugar, if you’re feeling fancy.