Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans. Line the bottoms with parchment paper.

In a medium bowl, whisk together the sifted flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, using an electric mixer, cream together the softened butter and granulated sugar until light and fluffy, about 3-5 minutes.

Add the eggs one at a time, beating well after each addition until fully incorporated. Scrape down the sides of the bowl as needed.

In a separate small bowl, combine the coconut milk and vanilla extract.

Alternately add the dry ingredients and the coconut milk mixture to the butter mixture, beginning and ending with the dry ingredients (3 additions of dry, 2 additions of wet). Mix on low speed until just combined after each addition. Do not overmix.

Fold in the 1/2 cup unsweetened shredded coconut with a rubber spatula.

Divide the batter evenly between the two prepared cake pans.

Bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean.

Let the cakes cool in the pans on a wire rack for 10-15 minutes, then invert them onto the wire rack to cool completely.

In a medium saucepan, whisk together 1 cup of the coconut milk, heavy cream, and granulated sugar over medium heat until the sugar dissolves and the mixture begins to simmer gently. Do not boil.

In a separate medium bowl, whisk together the remaining 1/2 cup coconut milk, cornstarch, and egg yolks until smooth.

Slowly pour about half of the hot coconut milk mixture into the egg yolk mixture, whisking constantly to temper the yolks.

Pour the tempered egg yolk mixture back into the saucepan with the remaining hot coconut milk mixture.

Cook over medium-low heat, whisking constantly, until the custard thickens significantly and coats the back of a spoon, about 5-8 minutes. Bring it to a gentle boil for 1 minute while continuing to whisk to ensure the cornstarch is cooked through.

Remove from heat and stir in the unsalted butter, vanilla extract, and 1/4 cup unsweetened shredded coconut until the butter is melted and fully incorporated.

Transfer the custard to a clean bowl, cover the surface directly with plastic wrap to prevent a skin from forming, and chill in the refrigerator for at least 2 hours, or until completely cold and firm.

Once the cake layers are completely cool and the custard is chilled and firm, level the cake layers with a serrated knife if necessary.

Place one cake layer on your serving plate or cake stand. Spread about half of the coconut custard evenly over the top of the first cake layer, leaving a small border.

Carefully place the second cake layer on top. Spread the remaining custard over the top of the second cake layer.

Preheat oven to 325°F (160°C). Spread the 1 cup shredded sweetened coconut flakes evenly on a baking sheet.

Toast in the preheated oven for 5-10 minutes, stirring occasionally, until golden brown and fragrant. Watch carefully to prevent burning.

Let the toasted coconut cool completely.

Generously sprinkle the cooled toasted coconut flakes over the top and sides of the assembled cake.

Refrigerate the cake for at least 30 minutes before slicing to allow the custard to set further and the flavors to meld.