Put the butter and sugar in a blender bowl and blend using the paddle attachment for about 20 minutes on high speed until the mixture is fluffy.
Add the vanilla extract, cognac, and crushed mastic. Lower the speed and blend for 10 minutes.
Remove the bowl from the blender, add the baking powder and flour in batches, and stir well with a pastry spatula.
Once the mixture is firm, continue stirring by hand until the mixture is homogenized. Add the almond flakes and stir.
Shape the mixture into round 30-35 grams (about 1 oz) shortbreads and press them with your finger slightly on top to flatten them.
Transfer the shortbreads to a baking pan lined with baking paper and bake for about 17 minutes, depending on their size.
Remove the cookies from the oven and let them cool well.
Place a sufficient amount of powdered sugar in a bowl then add the cookies a few at a time, turning them until completely covered.