Preheat the oven to 350°F (175°C) and grease two 8-inch round cake pans.
Sift the flour, baking powder, and salt together in a medium bowl and set aside.
Cream the softened butter and sugar in a stand mixer on medium-high speed until light and fluffy (about 5 minutes).
Add the eggs one at a time, beating well after each addition, then stir in the vanilla extract.
With the mixer on low, alternate adding the dry ingredients and the milk, beginning and ending with the flour mixture.
Divide the batter evenly between the prepared pans and smooth the tops.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Cool the cakes in the pans for 10 minutes before transferring them to a wire rack to cool completely.