Mardi Gras Tie-Dye Cake

Ingredients

• For the cake:
• 11 1/2 ounces all purpose flour, plus more for flouring pans
• 1 tablespoon baking powder
• 1/2 tablespoon salt
• 11 1/2 ounces sugar
• 16 tablespoons unsalted butter, softened and divided into 1 tablespoon pieces, plus more for greasing pans
• 4 large eggs, room temperature
• 2 yolks from large eggs, room temperature
• 1 tablespoon vanilla extract
• 1 1/4 cups whole milk, room temperature
• Green, yellow, and purple food coloring
• For the cream cheese frosting:
• 5 ounces sugar
• 1/4 cup cornstarch
• 1/4 teaspoon Kosher salt
• 1 large egg
• 1 egg yolk from a large egg
• 8 ounces whole milk
• 2 teaspoons vanilla extract
• 16 tablespoons unsalted butter, room temperature
• 8 tablespoons cream cheese, room temperature
• 2 tablespoons lemon juice from one lemon

Directions

1. Place a rack in the center of the oven and heat it to 350 degrees F. Butter and flour 3 cake pans, then keep them nearby. In a medium bowl, whisk the flour with the baking powder and salt; you’ll use this dry mix in a bit.
2. Using a stand mixer with the paddle attached, beat the butter and sugar on high until the mixture looks pale and airy, about 5 minutes. Drop the speed to medium, then work in the eggs and yolks 1 at a time, letting each disappear before adding the next and stopping to scrape the bowl with a rubber spatula as needed. After the eggs are in, blend in the vanilla. With the mixer on low, add the dry mixture and the milk in alternating thirds, mixing only until the batter comes together.
3. Divide the batter among 3 medium bowls. Tint the first bowl with drops of food coloring until the green looks right to you. Color the other bowls purple and yellow the same way.
4. Add dollops of the different batters to the prepared pans, scattering the colors as you go. Keep the total amount of batter even among the 3 pans. When all the batter is portioned, gently tilt each pan back and forth so it levels itself and the surface smooths.
5. Bake for 25-27 minutes, turning the pans halfway through the baking time, until the layers are golden brown, bounce back when touched, and a cake tester pushed into the center comes out clean. Let the cakes rest in their pans for 15 minutes, then ease them out onto cooling racks and leave them until fully cool. Wait to build the cake until the layers are cold all the way through.
6. For the frosting, put the sugar, cornstarch, and salt in a medium bowl, add the egg and egg yolk, and whisk until smooth and fully combined. Set this bowl aside.
7. In a small saucepan, whisk the milk with the vanilla extract, then warm it over medium heat just until tiny bubbles show up around the rim. Take the pan off the burner. While whisking quickly, pour half of that hot milk into the sugar-egg mixture so the eggs ease into the heat. Scrape the warmed eggs into the saucepan holding the rest of the milk, return the heat to medium, and keep whisking until it becomes as thick as pudding. When it is thick and bubbling, whisk for 1 minute longer, then pull it from the heat. Move the custard into a large bowl, or into the bowl for your stand mixer. Add the whisk attachment and beat on high until the custard is fully cooled; truly, it needs to be cold before the butter goes in. If you have time to spare, press plastic wrap on the surface and chill it until cold.
8. When the custard has cooled, turn the mixer to high. Beat in the butter in 1 tablespoon pieces, waiting briefly after each addition so it can blend in. Follow with the cream cheese, also adding 1 tablespoon at a time, and keep mixing until the frosting turns airy and smooth. Mix in the lemon juice until it disappears into the frosting.
9. Frost the cake, spreading only a thin coat between layers so there is enough frosting left to cover the top and sides. Chill it for 1 hour before you serve it, which helps the frosting set. Keep the cake covered in the refrigerator.