Step 1
Preheat the oven to 350 degrees F (175 degrees C). Grease and lightly flour three 9-inch metal cake pans.
Step 2
Sift cake flour baking powder and salt for cake into a bowl and set aside. Whisk eggs coconut milk heavy cream and vanilla extract together in a small bowl until well combined.
Step 3
Cream sugar and butter together in a large bowl until light and fluffy scraping down as needed. Add 1/3 of the flour mixture and mix on low speed until incorporated. Add 1/2 of the milk mixture and mix on low until evenly incorporated. Repeat ending with remaining flour mixture scraping down the bowl after each addition and mixing at medium speed until well incorporated about 1 minute. Evenly split batter among the prepared cake pans.
Step 4
Bake in the preheated oven until a toothpick inserted into the center comes out clean and cakes are starting to pull away from the sides of the pans 30 to 40 minutes. Allow to cool in the pans for 5 to 10 minutes; invert onto a cooling rack to cool completely about 30 minutes.
Step 5
While cakes cool make lemon curd. Mix sugar and cornstarch well in a small bowl and set aside. Whisk whole eggs and egg yolks together in a small bowl and set aside.
Step 6
Heat lemon juice and zest in a small saucepan over medium-low heat until hot. Add sugar and cornstarch mixture all at once. Bring back to a simmer stirring constantly. Whisk some of the hot lemon mixture into the eggs to temper them. Pour back into the saucepan. Cook stirring constantly until thick 5 to 10 minutes.
Step 7
Remove curd from heat and add butter. Mix until smooth. Strain curd if necessary and place in a small bowl. Press plastic wrap against the surface and chill at least 20 minutes.
Step 8
Meanwhile make pastry cream. Mix sugar and cornstarch together in a small bowl. Whisk egg and egg yolk together in a small bowl until well mixed.
Step 9
Heat coconut milk in a small saucepan until simmering. Add sugar-cornstarch mixture and whisk until smooth and sugar is melted. Whisk some of the hot milk into the eggs to temper them. Pour back into the saucepan and cook stirring constantly until thickened 3 to 5 minutes.
Step 9
Remove pastry cream from heat and stir in butter and coconut rum; mix until smooth. Strain if necessary cover with plastic wrap and refrigerate until cold about 20 minutes.