Preheat the oven to 350F (180C). Line a 12-cavity muffin tin with cupcake papers. Set aside.
In a medium bowl, whisk together the flour, baking powder, salt and desiccated coconut. Set aside.
In a large bowl, beat together the butter and sugar until creamed (you should no longer see lumps or pieces of butter).
Beat the eggs into the butter mixture one at a time. Turn off the mixer and scrape down the bottom and sides of the bowl after mixing in each egg.
With the mixer on a low speed, beat about 1/3 of the flour mixture into the butter mixture. Then beat in about 1/2 of the coconut milk. Repeat the process, beating in about 1/3 of the flour mixture, followed by the rest of the coconut milk. Finally, beat in the rest of the flour mixture. Do not overmix the batter. After each addition, stop mixing as soon as everything is incorporated. Turn off the mixer and scrape down the sides of the bowl as needed.
Spoon the cupcake batter into the prepared muffin tin, filling each muffin cavity about 2/3 full to 3/4 full. You should get about 12 cupcakes.
Bake the cupcakes in the middle of the preheated oven for about 19-23 minutes, or until the tops look set and an inserted toothpick comes out clean
Cool the cupcakes in the pan for at least 5 minutes before carefully transferring to a wire rack to continue cooling.