Preheat your oven to 375°F. Line two baking sheets with parchment paper and set aside.
In the bowl of a stand mixer, beat together the butter and sugar until light and fluffy, about 3 minutes.Add the eggs, one at a time, scraping the bowl down after each addition.
Slowly drizzle in the milk (to avoid splatters), then the vanilla and mix until combined.
In another large bowl, whisk together the flours, baking powder, and salt. Add the dry mixture to the wet ingredients a little at a time, until all has been added.
Using a cookie scoop or 2 large spoons, scoop roughly ¼ cup portions out onto the prepared cookie sheets, leaving at least 2 inches of space between each cookie. Bake for 18 to 20 minutes, until the cookies are only just beginning to brown. Allow to cool completely before icing.