Preheat the oven to 350 and prepare two round 8 inch cake pans.
Begin with the dry ingredients in the mixer - flour, sugar, baking powder, and salt. Add in the butter a little bit at a time until the mixture is crumbly.
In a medium bowl, whisk the egg whites, coconut milk, shredded coconut and vanilla bean paste. Add half of this mixture to the flour/butter crumble and stir on low. Scrape the sides of the bowl and add the remaining liquid to the mixer.
Divide the batter between the pans and bake for 35 minutes. Let cool.
For the Frosting
Place the sugar and egg whites in your mixer bowl and place it over simmering water to make a double boiler. Whisk it over the heat for 8 minutes - it should be warm to the tough in the center.
Move your bowl to the mixer and attach the whisk. Turn the mixer to medium high and let it run for 5 minutes. The sides of the bowl should cool and the mixture will get thick, glossy and pure white. Keep it running for another 3 - 5 minutes and make sure it's cool.
Turn the mixer to low and gradually add 1 tablespoon of butter at a time. The mixture will look curdled and scare you if you've never made a meringue frosting before. Just keep whipping.
Add the extract, salt and coconut milk and whip for 2 - 4 minutes to incorporate everything. Your frosting should be thick and fluffy.
To Assemble the Cake
Torte and level your cakes. Place a cup of frosting into a piping bag and make a dam around the perimeter. Use ⅓ of the pudding in the center and spread it around. Add a second layer of cake and repeat until all the pudding is used and 4 layers of cake are on.
Frost the cake completely and then take a handful of shredded coconut and press it into the frosting. A lot will fall off and that's fine. Just scoop it back up and keep adding until the cake is covered. You will only use about half the bag of shredded coconut.
Clean up the platter and top the cake with the Macaroons.