Preheat your oven to 350°F (175°C). Grease and flour three 8-inch round cake pans.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, followed by the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk, beginning and ending with the dry ingredients. Mix until just combined.
Divide the batter evenly among the prepared cake pans and smooth the tops with a spatula.
Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted into the center of the cakes comes out clean.
Allow the cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.