Preheat oven to 350°F. Grease and line with parchment paper 2 (9-inch) round cake pans. (I used non-stick cooking spray before and after placing a parchment paper circle which I cut out myself after tracing the line of the pan onto the paper. Or you can buy them pre-cut.) Set aside.
Place cake flour, baking powder and salt in a medium bowl. Whisk until combined. Set aside.
In a large bowl, beat butter and sugar with an electric mixer on medium until light and fluffy, about 2 minutes. With mixer on low, gradually add eggs (one at a time). Turn mixer to medium and beat for 30 seconds or until eggs are completely mixed in.
Combine milk and vanilla in a small bowl, then with mixer on low, alternate adding milk mixture and flour mixture. Add about a third of the flour, then a third of the liquid. Mix until combined. Repeat with remaining dry and wet ingredients. Once all of the cake ingredients are combined, turn mixer up to medium and beat for about 30 seconds.
Pour batter into prepared pans, dividing the batter equally between the two. Bake for 30-35 minutes or until a toothpick inserted into the middle comes out clean. Let cool.