To make the cake layers:

1. Using an electric mixer (a stand mixer or handheld), beat the butter and sugar at medium speed until light and creamy, about 3 minutes.
2. Add eggs two at a time, mixing on low speed to incorporate after each addition.
3. Add coconut milk and vanilla and mix at medium speed.
4. Add flour and baking powder and mix on the lowest speed until just combined.
5. Divide batter between three greased 6" cake pans and bake at 325F or 160C for 35 minutes or until cakes spring back up when poked in the middle.
6. Leave cakes in their pans for 10 minutes before turning out onto a cooling rack and let them cool completely.

To make the coconut filling and frosting:

1. Put flour, milk and salt in a pan and cook over medium heat for about 5 minutes. Whisk it constantly until it simmers to prevent lumps. Once it simmers, switch to a spatula and continue to stir, scraping around the sides and bottom of the pan. Stir for about 2 minutes until the mixture thickens enough to leave ribbons when you lift the spatula.
2. Remove the pan from the heat and pour into a heatproof bowl. Stir in vanilla and cover the bowl with plastic wrap (e.g. cling film / Saran Wrap), pressing it down to touch the surface of the mixture. Put it into the fridge for about an hour to cool to room temperature.
3. Mix butter and sugar at medium speed until creamy and lighter in colour, about 3 minutes. Add cooled flour mixture and mix for another minute, until smooth.

To put the cake together:

1. Spread a bit of coconut frosting onto the middle of a cake board or plate and press your first cake layer down to attach it. Spread coconut frosting to cover the top of the cake and then place then final cake layer on top.
2. Put the cake in the fridge for 30 minutes or the freezer for 15 minutes to chill and set. Then spoon about half of the remaining coconut frosting on top and spread with an offset spatula or palette knife to cover the cake. Use a straight edged cake comb or frosting smoother to smooth the frosting but it doesn't need to be perfect yet! Chill in the fridge for another 30 minutes or freezer for 15 minutes to set this crumb coat of frosting.
3. Spoon the rest of the coconut frosting onto the cake and spread to cover the cake. Smooth or add texture with a textured cake comb. Optionally, spoon the leftover frosting into a piping bag fitted with any star tip (I used a 4B) and pipe a border around the top of the cake.
4. You can refrigerate this cake for 3 days but take it out 2 hours before serving so that the cake and frosting come to room temperature.