Preheat your oven to 350°F (175°C).
Line two 9-inch round cake pans with parchment paper and grease the sides.
In a mixing bowl, sift together flour, baking powder, and salt. Set aside.
In another large bowl, cream the butter and sugar until light and fluffy (about 3 minutes).
Add eggs one at a time, mixing well after each addition. Stir in vanilla extract.
Alternate adding the dry ingredients and milk to the butter mixture, starting and ending with the dry ingredients. Mix until just combined.
Divide the batter evenly between the two pans and smooth the tops.
Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean.
Let the cakes cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely.