Cream granulated sugar with room temperature butter and coconut oil(solid form) on LOW speed.
Blend in egg, egg WHITE and extracts on MEDIUM speed until light and fluffy.
Sift cake flour with the baking powder, cream of tartar and salt.
Gradually add to the wet mixture until well incorporated.
Place in a sealed container and chill for at least 3 hours.
Using a medium cookie scoop, create about 36 mounds of dough. Roll them in cake flour then between the palms of your hands into a ball.
Place them on a parchment paper-lined rimmed baking sheet 3" apart. Flatten to a height of 1/2" using a floured flat-bottomed glass.
Bake at 375°F for 8 minutes. They will be pale and slightly puffy, but don't bake any longer!
Put pan on a cooling rack for 3 minutes. Then, remove cookies to cooling rack to completely cool, before frosting.