This is a Martha Stewart recipe and produces a very rich dense butter cake. Because of the richness of it, I would use this more to serve with fruit and cream (like a pound cake) rather than a birthday layer cake.
Preheat oven to 350°. Butter one 10-inch tube pan. Dust the bottom and sides of pan with flour, and tap out any excess. Sift together flour, baking powder, baking soda, and salt; set aside.
In the bowl of a standing mixer fitted with the paddle attachment, beat butter until softened, 1 to 2 minutes. Gradually add sugar, and continue beating until light and fluffy, about 4 minutes. Add eggs one at a time, beating after each addition until well incorporated, occasionally scraping down the sides of bowl.
Mix together buttermilk and vanilla. Slowly add the sifted flour mixture alternately with the buttermilk mixture in three additions, beginning and ending with the flour mixture. Do not overbeat.
Pour batter into prepared tube pan, and until cake tester inserted into center of cake comes out clean, about 40 minutes. Transfer to a wire rack to cool for 15 minutes. Remove cake from pan, and cool completely on wire rack. Cake can be stored in freezer, double wrapped with aluminum foil, for up to 1 month.