Keep the oven at 350 degrees F (as it was for roasting the coconut and almonds). Grease a 9x9-inch cake pan. I also like to line it with a sheet of parchment, leaving strips up the sides for easy removal. Set aside.
In a medium bowl, add the flour, baking powder and salt. Whisk until combined. Set aside.
To the bowl of a stand-up mixer with the paddle attachment, add the butter, oil, coconut extract and sugar. Beat until light and fluffy, about 2 to 3 minutes. In a measuring cup, pour in the milk, egg whites and whisk until combined.
Turn the mixer to low speed and, alternating between the dry ingredients and the liquid ingredients (the egg white mixture), add them to the butter/sugar mixture until the batter is relatively smooth. Add the reserved crushed up coconut flakes and almonds and gently fold into the batter.
Pour the batter into the prepared baking pan and transfer to the oven to bake for 20 to 25 minutes, until a skewer inserted into the center comes out clean.
Allow the cake to cool in the pan for about 5 minutes and then invert onto a cooling rack and cool to room temperature. It’ll probably take a good hour.