In the bowl of a stand mixer, or by hand, beat the butter, coconut oil, and sugars together for about 5 minutes or until light and fluffy.
Add the egg and both extracts and mix.
In a separate bowl, mix the flour, baking powder and salt. Add to mixer bowl and mix until combined.
Press the mixture into the bottom of the prepared pan, smoothing the edges straight.
Bake for 15 minutes or until done. The cookie should be lightly golden.
Let cool completely. Then run a spatula or knife alongside the edges, to loosen the cookie. (You can remove the whole cookie layer from the pan now, to a cutting board, add the frosting and coconut, and then cut it, before adding it back to the pan or a serving plate, if you do not want to cut directly in your baking pan)
For Frosting Layer
Beat the butter, coconut oil, vanilla, and salt until light and fluffy.
Add the powdered sugar and beat again until light and fluffy. Add milk, a little at a time, until desired consistency (I like a light, smooth frosting)
Spread the frosting on top of the cooled cookie layer.
Heat a skillet over medium heat. Add the coconut, and then heat, stirring the coconut regularly, until toasted, about 8-10 minutes.
Sprinkle the coconut on top of the frosting and refrigerate until serving.
Notes
To omit the coconut oil, replace it with the same amount of butter.