Begin by greasing and flouring three 8-inch round cake pans. For extra ease, line the bottom of each pan with parchment paper.
Preheat your oven to 350°F (175°C).
In a medium-sized bowl, whisk together the cake flour, baking powder, and salt. Set this dry mixture aside for later use.
Using an electric mixer fitted with a paddle attachment, cream the softened butter on medium speed until it becomes smooth. Gradually add the sugar and continue to beat until the mixture turns light and fluffy, which should take about 3 to 5 minutes.
Incorporate the eggs one at a time, mixing thoroughly after each addition until the yolks are well blended into the batter.
Stir the vanilla extract into the buttermilk.
With the mixer set to low speed, add the flour mixture to the butter and sugar batter alternately with the buttermilk. Start and finish with the dry ingredients, making three additions of the dry mix and two of the buttermilk.
Evenly divide the cake batter among the three prepared pans.
Bake in the preheated oven for 20-25 minutes or until a toothpick inserted into the center of the cakes comes out clean or with just a few moist crumbs. You can also test doneness by gently pressing the center of the cake; it should spring back when touched. Baking times may vary slightly.
Allow the cakes to cool in the pans on a wire rack for 10 minutes before carefully inverting them onto the rack to cool completely.