Preheat the oven to 350°F (175°C). Grease and line two 9-inch cake pans.
Whisk together the flour, baking powder, and salt.
Cream the butter and sugar until light and fluffy, about 3 minutes.
Beat in the eggs one at a time, then add the vanilla.
Alternate adding the dry ingredients and milk, beginning and ending with the flour mixture. Mix just until combined.
Divide the batter evenly between the pans.
Bake for 25–30 minutes, until a toothpick inserted into the center comes out clean.
Cool in the pans for 10 minutes, then transfer to wire