Preheat oven to 350ºF, and make sure the rack is in the center of the oven.
Line just the bottom of 2 round cake pans (8" or 9") with parchment paper.
Measure the flour, baking powder and salt into a medium bowl and whisk together or sift together. Set aside.
With an electric mixer, mix the butter and sugar together on medium speed until pale and fluffy, 3 - 5 minutes. Stop halfway through mixing and scrape down the bowl.
Add the eggs one at time, beating slightly after each addition.
Mix in the vanilla until blended.
Reduce speed to low and add the flour mixture and milk alternately in 3 batches; starting and ending with the flour mix.
Mix until batter is just smooth, do not over mix.
Pour batter into the prepared pans and smooth the tops.
Bake for 20 - 25 minutes.
Cake is done when a toothpick or knife inserted into the center comes out clean.
Remove from oven, and set the pans on a cooling rack. Run a knife around the edge to loosen the cake from the pan. Cool for 7 - 10 minutes, then turn out onto rack to finish cooling. Peel parchment paper off of cake. (You can also peel the parchment when the cake is still warm.)
Frost when cake is completely cool.