Preheat oven to 350 degrees.
Start by creaming ½ cup + 2 tablespoon of butter and 1 ½ cups of granulated sugar together in a large bowl.
Next add in 3 eggs and 1 ½ tablespoon vanilla bean paste. Mix until combined.
Then add in 1 cup of buttermilk and combine.
In a separate, medium sized bowl, sift 2 ¼ cups of cake flour, ½ teaspoon of salt, 1 ½ teaspoon of baking powder and ¼ teaspoon of baking soda together.
Add the dry ingredients to the wet ingredients a little at a time. Continue until everything is combined together.
Divide the batter evenly between 3 6″ greased cake pans.
Bake the cakes at 350 degrees for 35-38 minutes, or until a toothpick comes out clean from the centers.
Let the cakes cool in their pans for five minutes and then transfer them to a cooling rack to finish cooling completely.