Place an oven rack in the center of the oven. Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with paper liners. Set aside.
In a medium bowl, whisk together the flours, baking powder and salt.
In a large bowl, using an electric hand mixer, beat the sugar and butter until combined. Add the eggs, milk and vanilla. Beat until smooth. Add the dry ingredients and mix until just blended. Spoon the batter into the prepared muffin cups (about 1/4 cup batter in each cup). Bake until puffed and the cake springs back when touched, 15 to 17 minutes. Transfer to a wire rack and cool completely, about 30 minutes.
Using a small spatula, frost the tops of the cupcakes. Allow the frosting to set for 20 minutes before serving.