Preheat the oven to 350°F (175°C).
Butter and flour two standard 8-inch (20-cm) round cake pans. Line the bottom of the pans with parchment paper cut to fit.
In a medium bowl, whisk together the egg yolks, 1/2 cup of the milk, and the vanilla.
In the bowl of a stand mixer fitted with the paddle attachment on low speed, mix the flour, granulated sugar, baking powder, and salt for about 30 seconds. Add the remaining 1/4 cup milk and mix until just moistened, about 15 seconds.
Add the butter and beat on medium speed until smooth and aerated, 1 1/2 to 3 minutes. Scrape down the sides of the bowl with a rubber spatula. Add the egg mixture in 3 batches, mixing on medium speed for 20 seconds and scraping down the bowl after each addition.
Scrape the batter into the prepared pans and smooth the surface with an offset spatula. Bake, rotating the pans once during baking, until the cake springs back when gently pressed in the center or until a toothpick inserted in the center comes out clean, 25 to 30 minutes.
Let the cake cool in the pans on a wire rack for 30 minutes. Then run the spatula around the edges of the pans. Invert the cakes onto the wire rack and remove the pans and parchment paper. Let cool until you can handle them, about 20 minutes.
Gently turn the cakes again so they're right side up. Let cool completely, wrap tightly in plastic wrap, and refrigerate for at least 3 hours before assembling.