Preheat your oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, beat the butter until it's creamy and light in color, about 2 minutes. Gradually add the sugar, beating continuously, until the mixture is fluffy and well incorporated, about 3-4 minutes.
Add the eggs, one at a time, beating well after each addition. Make sure to scrape down the sides of the bowl as needed. Stir in the vanilla extract.
Add the flour mixture in three parts, alternating with the milk, beginning and ending with the flour. Beat on low speed until just combined; do not overmix.
Divide the batter evenly among the prepared cake pans, smoothing the tops with a spatula.
Bake for 25-30 minutes, or until a toothpick inserted into the center of the cakes comes out clean. Let the cakes cool in the pans for 10 minutes, then remove from the pans and transfer to a wire rack to cool completely.