For the cake: Position a rack in the center of the oven and preheat to 325 degrees F. Line the bottoms of two 8-inch cake pans (each 3 inches deep) with parchment circles. Lightly spray the pans with nonstick cooking spray and set aside.

Whisk the coconut milk, oil, pandan paste and vanilla together in a measuring cup with a spout until smooth. Set aside.

Sift the cake flour and salt together into a medium bowl. Set aside.

Whip the egg yolks, whole egg and ½ cup of the sugar in the bowl of a stand mixer fitted with a whisk attachment on medium-high speed until tripled in volume and light in color, about 4 minutes. Reduce the speed to low and alternate stirring the flour mixture in one-third at a time, alternating with the pandan-coconut milk mixture in 2 additions, starting and ending with the flour. Mix until just smooth; a few pockets of flour are okay. Remove the bowl from the mixer and fold the batter with a rubber spatula until no streaks of yellow remain. Transfer all the batter into a large bowl. Set aside.

Wash the stand mixer bowl and whisk attachment thoroughly, making sure to remove any trace of fat, then dry both thoroughly. Add the egg whites and cream of tartar to the cleaned bowl and beat with the clean whisk attachment on medium speed until foamy and doubled in size, about 2 minutes. Slowly sprinkle the remaining ½ cup sugar into the bowl while the mixer is running. Increase the speed to medium high and continue whisking until the meringue holds stiff peaks, about 3 minutes.

Fold the meringue into the batter in 2 additions, folding until just combined and no streaks of meringue remain. Divide the batter between the prepared cake pans; the batter will reach about three-quarters of the way up the pans but will not overflow during baking. Smooth the tops with a small offset spatula, then gently tap the cake pan on the work surface to remove any large bubbles. Bake until the tops are golden and the cakes spring back when gently pressed, about 45 minutes.

Carefully remove the cakes from the oven. Flip both cake pans upside-down over a cooling rack and let them cool completely on the rack, about 1 hour. Run a paring knife along the sides of the cake pans to release, flip the cakes onto the rack and remove the parchment circles. The cakes will be slightly concave in the center. Level the concave part of the cakes with a serrated knife. Set aside.

Meanwhile, make the coconut pastry cream: Bring the coconut milk, heavy cream and 2 tablespoons sugar to a simmer in a medium saucepan over medium heat. Whisk the remaining 2 tablespoons sugar, egg yolks and cornstarch in a medium bowl until smooth and lightened in color.

While whisking constantly, carefully pour the hot milk into the egg mixture in small additions until the egg is warm and smooth. Pour the egg mixture back into the saucepan and cook over medium heat, whisking constantly, until thickened, about 3 minutes. Whisk the butter, coconut extract and vanilla extract in until smooth. Strain the pastry cream through a fine-mesh strainer into a bowl. Cover with a sheet of plastic wrap touching the surface of the pastry cream and refrigerate until chilled, about 1 hour.

When both the pastry cream and cake layers are cooled, make the coconut whipped cream: Whisk the heavy cream, coconut milk, confectioners’ sugar, milk powder, coconut extract and vanilla extract together in the bowl of a stand mixer fitted with a whisk attachment on medium speed until the sugar is dissolved, about 1 minute. Increase the speed to medium high and whip until medium peaks form, about 3 minutes. Refrigerate the whipped cream while you assemble the cake.

To assemble, stir the chilled pastry cream with a rubber spatula until smooth and set aside. Lay one pandan cake layer on a cake stand and spread the top evenly with the pastry cream. Top with the remaining cake layer. Frost the top and sides of the cake with the coconut whipped cream. Chill the frosted cake in the refrigerator for at least 2 hours before slicing and serving.