Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, or line them with parchment paper.
Mix dry ingredients: In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
Cream butter and sugar: In a large bowl, beat the softened butter and sugar together with an electric mixer on medium speed until light and fluffy, about 3-5 minutes.
Add eggs and vanilla: Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Add dry ingredients and milk: Add the dry ingredients in three parts, alternating with the milk. Start and end with the dry ingredients. Mix until just combined; do not overmix.
Bake: Divide the batter evenly between the prepared cake pans. Smooth the tops with a spatula. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Cool: Allow the cakes to cool in the pans for about 10 minutes. Remove from the pans and transfer to a wire rack to cool completely before frosting.
