For the cupcakes: Preheat the oven to 325 degrees F and line muffin pans with paper liners.
In a medium bowl, sift the cake flour, granulated sugar, baking soda and salt.
In the bowl of an electric mixer fitted with the paddle attachment, combine the oil, buttermilk, coconut milk, vanilla and eggs. Mix until all the ingredients are fully combined, about 1 minute. Slowly add the dry ingredients to the wet ingredients and mix only until all the ingredients are barely incorporated. Fold in the shredded coconut. Fill the liners about three-quarters of the way full and bake, 17 to 19 minutes.
Let the cupcakes cool slightly before removing them from the pan and transferring to a cooling rack.
For the lime curd: In the bowl of an electric mixer, beat the butter and granulated sugar until light and fluffy. Slowly add the eggs and yolks, and then beat until combined. Add the lime juice. The mixture WILL look curdled. Do not fear, it will smooth out as the butter melts when you cook the mixture.
In a stainless steel saucepan, cook the mixture over low heat until it smooths out. Increase the heat to medium and cook, stirring constantly, until the mixture is thick, 10 to 12 minutes. Do not let it boil. Remove the curd from the heat and stir in the lime zest. Put the curd in a clean bowl and wrap it tightly. Place in the fridge until cool, about 1 hour.
For the frosting: In electric mixing bowl with paddle attachment, beat the butter until fluffy and pale in color. Add the powdered sugar gradually and beat until fully combined. Drizzle in the coconut milk and rum. Add more powdered sugar or coconut rum to adjust the consistency of the frosting.
Core out the center of the cupcakes, fill with lime curd and frost with coconut rum frosting.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.