In a medium bowl, whisk the cake flour, baking powder and salt. In another medium bowl, whisk the coconut milk with the whole milk and coconut extract. In a stand mixer fitted with the paddle, beat the 2 sticks of butter with the granulated sugar at medium speed until fluffy, about 2 minutes. At medium-high speed, beat in the egg whites in 3 additions. At low speed, beat in half of the dry ingredients until nearly incorporated. Beat in the wet ingredients, then beat in the remaining dry ingredients until just incorporated; scrape down the side of the bowl as needed.