Choose your pan, depending on whether you'll be making: a 9x3-inch round springform pan (for layer cakes), an 8x2-inch square cake pan (for trifles), or a 13x18-inch rimmed baking sheet (for roulades); line the bottom of the pan with parchment. Position a rack in the lower third of the oven, and heat the oven to 350°F for a round or square pan or to 400°F for a baking sheet.
Whisk the flour and baking powder in a medium bowl.
With an electric mixer (hand-held or a stand mixer fitted with the whisk attachment), beat the eggs, yolks, sugar, vanilla, and salt at high speed until the mixture has tripled in volume and forms a slowly dissolving ribbon when the stopped beater(s) are lifted, 4 to 6 minutes.
Meanwhile, heat the milk and butter in a small saucepan over medium heat until very hot but not boiling.
Using a fine-mesh sieve, sift one-third of the flour over the eggs. Fold with a large silicone spatula until the flour is blended into the batter. Repeat with two more batches.
Pour all of the hot milk mixture over the batter and fold gently with the silicone spatula, scraping the batter up from the bottom of the bowl and rotating the bowl, until the milk is incorporated. Scrape the batter into the pan and spread evenly.
Bake until the cake is golden and a tester inserted into the center comes out clean, 20 to 25 minutes for the round or square cake pans, or 10 to 12 minutes for the baking sheet. Set the pan on a rack to cool. After the cake has cooled completely, run a small knife or offset spatula around the inside of the pan, pressing against the pan to avoid tearing the cake. Invert the pan to remove the cake, and peel off the parchment liner. Turn the cake right side up.
Make Ahead Tips
A cake baked in the round or square pan may be wrapped airtight and stored at room temperature for 2 days or frozen up to 3 months.
A sheet cake should be made into a roulade within 24 hours. Otherwise it may dry out and crack when rolled. If you’re not using it right away, wrap it airtight and store at room temperature.