Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the sifted flour, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter on medium speed until creamy, about 1 minute.
Gradually add the granulated sugar to the butter and continue beating on medium-high speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition to incorporate fully.
Mix in the vanilla extract until combined.
With the mixer on low speed, alternately add the flour mixture and the milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined; do not overmix.
Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula.
Bake in the preheated oven for 28-30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and let them cool in the pans for 10 minutes.
Run a knife around the edges to loosen, then invert the cakes onto wire racks to cool completely before frosting or serving.