Preheat oven to 325F. Grease and flour three 8" cake rounds and line with parchment.
In a medium bowl, whisk flour, baking powder, and salt until well combined. Set aside.
Using a stand mixer fitted with a paddle attachment, cream butter and lime zest until smooth. Add sugar and beat on med-high until pale and fluffy (approx 3mins).
Reduce speed and add eggs one at a time fully incorporating after each addition. Add vanilla.
Alternate adding flour mixture with milk, beginning and ending with flour (3 additions of flour and 2 of milk). Fully incorporating after each addition. Gently fold in shredded coconut.
Spread batter evenly between the prepared pans and smooth the tops.
Bake for about 35mins or until a toothpick inserted into the center comes out mostly clean.
Place cakes on wire rack to cool for 10mins then turn out onto wire rack to cool completely.
Place eggs and sugar into a small pot, whisk to combine. Add lime juice and zest. Cook over medium-low heat whisking constantly until mixture thickens and coats the back of a spoon. Stir in cubed butter and whisk until smooth.
Transfer to a glass bowl and lay plastic wrap directly on surface to prevent a skin from forming. Chill for 2 hours to set. Makes a little over 1 cup.
Coconut Swiss Meringue Buttercream:
Place egg whites and sugar into the bowl of a stand mixer, whisk until combined.*
Place bowl over a pot with 1-2" of simmering water and whisk constantly until the mixture is hot and no longer grainy to the touch or reads 160F on a candy thermometer (approx. 3mins)
Place bowl on your stand mixer and whisk on med-high until the meringue is stiff and cooled (the bowl is no longer warm to the touch (approx. 5-10mins)).
Switch to paddle attachment. Slowly add cubed butter and mix until smooth.**
Add 6-8 Tbsp coconut milk powder (to taste) one Tbsp at a time whip until smooth.
Place one layer of cake on a cake stand or serving plate. Poke holes into the cake using a bamboo skewer. Brush with simple syrup if desired.
Spread a thin layer of buttercream on top of the layer and pipe a border around the outside to hold the lime curd in. Fill with about 1/2 cup of lime curd. Repeat with next layer.
Place final layer on top and do a thin crumb coat on the cake. Chill for 20mins.
Frost the top and sides of the cake with remaining frosting. Smooth the sides and top and do a rope border with the remaining buttercream. Fill the center with large toasted coconut chips and sprinkle with lime zest if desired.
* Ensure there is NO trace of egg yolks in your whites and that your mixer bowl and whisk is completely grease free or your meringue won't stiffen. ** The buttercream may look like it's curdled at some point. Keep mixing until it is completely smooth.