Preheat oven to 350 F. Line grease and line the bottoms of two 8-inch round pans with parchment paper. Position oven rack in the center of the oven.
In a large bowl, whisk together oil, egg yolks, water, pandan flavoring, green food coloring (if using), water, and milk.
Sift the dry ingredients (cake flour, 1/4 cup (50 g) sugar, baking powder, and salt) into the egg yolk batter. Whisk to combine.
In the bowl of a stand mixer using the whip attachment, or in a medium bowl using an electric hand mixer, beat the egg whites with cream of tartar at medium speed until frothy. Increase to high speed, then add the sugar gradually. Beat until a stiff peak forms.
Fold the beaten egg whites into the egg yolk mixture.
Pour the cake batter into the prepared pans and tap the filled cake pan on the counter to remove any large air bubbles.
Bake in the preheated oven for 25 minutes until the surface of the cake springs back when lightly touched and the edges begin to pull away from the side of the pan.
Remove from oven and let the cake cool on a wire rack for 10 minutes. Remove the cooled cake from the pan. If making ahead, wrap tightly in plastic wrap and store in the refrigerator or freezer until you are ready to frost.
Prepare the icing:
Beat the cream cheese and powdered sugar in a stand mixer using the paddle attachment until smooth.
Switch to the whisk attachment, and pour in the heavy cream. Beat until fluffy and a mousse-like texture forms.
Set aside a small bowl of the frosting to use for decorating.
Add the pandan extract and beat until well combined and no streaks remain. Put the pandan frosting in a piping bag with a half inch round tip.
Trim the cakes and place a cake layer on a cake stand. Pipe a thick layer of frosting over the cake, then top with the second cake. Pipe frosting over the top of the cake and sides and use an offset spatula or cake scraper to smooth the frosting.
Use the cake scraper to cover the sides of the cake with the flaked coconut.
Use a star tip to pipe decorations on the cake in green and white.
This cake keeps extraordinarily well in a airtight container in the refrigerator. Ours lasted for several days, until we couldn't keep our hands off it any longer.