Preheat oven to 350°F.
Grease two 9-inch round cake pans and line the bottoms with parchment paper.
In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, beat the butter and sugar until light and fluffy, about 2 to 3 minutes.
Add eggs one at a time, mixing well after each addition.
Stir in the vanilla extract.
Add the flour mixture in three parts, alternating with the milk, beginning and ending with flour.
Mix until just combined—do not overmix.
Divide the batter evenly between the prepared pans and smooth the tops.
Bake for 28 to 32 minutes, or until a toothpick inserted in the center comes out clean.
Let the cakes cool in the pans for 10 minutes.
Turn them out onto a wire rack to cool completely before frosting.