Preheat the oven to 350°F (175°C). Grease and line two 9-inch round cake pans with parchment paper.
Heat the milk and butter together until the butter melts. Keep warm.
In a medium bowl, whisk together the cake flour, baking powder, and salt.
Using a stand mixer or hand mixer, beat the eggs, sugar, and vanilla on high speed for about 5 minutes until pale, thick, and tripled in volume.
Fold the flour mixture into the egg mixture on low speed until just combined.
Transfer about 1½ cups of batter into a separate bowl and whisk in the warm milk mixture.
Pour the tempered batter back into the remaining batter and gently fold together.
Divide the batter evenly between the prepared cake pans.
Bake for 25–30 minutes until the cakes spring back lightly when touched.
Cool completely in the pans before removing.