Preheat oven to 350 degrees F (175 degrees C). Grease and flour 2 - 8 inch round pans. Sift together the flour, baking powder and salt. Set aside.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the egg yolks one at a time, then stir in the vanilla. Beat in the flour mixture alternately with the milk, mixing just until incorporated. Pour batter into prepared pans.
Bake in the preheated oven for 25 to 30 minutes, or until tops spring back when lightly tapped. Cool 15 minutes before turning out onto cooling racks.