Preheat the oven to 350°F (175°C). Grease and flour a 9-inch (23cm) round cake pan.
In a medium bowl, whisk together the sifted flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract.
With the mixer on low speed, alternately add the dry ingredients and the milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
Pour the batter evenly into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 28-32 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Run a knife around the edges to loosen the cake, then invert it onto a wire rack to cool completely before serving.