Preheat oven to 180 degrees C with rack in center of oven. Butter or spray with a non-stick vegetable spray, two 9-inch x 2 inch (23 x 5 cm) cake pans. Then line the bottoms of the pans with parchment or wax paper, then spray the paper.
In a bowl, sift or whisk together the flour, baking powder, and salt.
In the bowl of your electric mixer, with the paddle attachment, (or with a hand mixer) beat the butter until soft and creamy. Gradually add the sugar and beat until light and fluffy. Add eggs, one at a time, beating well after each addition
Scrape down the sides of the bowl as needed. Add the vanilla extract and beat until combined. With the mixer on low speed, alternately add the flour mixture (in three additions) and milk (in two additions), beginning and ending with flour.
Pour into pan. Bake 27 to 35 minutes or until a toothpick inserted into the center of the cake comes out clean and the cake springs back when pressed lightly in center.
Place the cakes on a wire rack to cool, in their pans, for about 10 minutes. Then invert the cakes onto a greased rack. Remove the parchment or wax paper and re-invert cakes so that tops are right side up. Cool completely before frosting.