Preheat oven to 350° F and lightly grease a 9x13” baking dish or cake pan. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine cake flour, sugar, baking powder, baking soda, and salt. Stir to combine.
In a large measuring cup, whisk together eggs, coconut milk, vanilla, and coconut extract (if using). Set aside.
Add room temperature butter and coconut oil to dry ingredients mix on medium speed until batter is coarse and resembles the texture of bread crumbs.
With the mixer on low speed, slowly stream in wet ingredients, mixing only until everything is homogenous and combined. Remove bowl from the mixer and fold with a rubber spatula to ensure no dry spots remain.
Pour about 1/3 of the batter into a small bowl and add the tablespoon of matcha powder. Stir to combine. Fold shredded coconut into the batter remaining in the large mixing bowl.
Pour coconut batter into the prepared pan. Dollop matcha batter on top and use the back of a knife to marble.
Bake for 30-40 minutes, rotating the pan halfway through the baking time, until a toothpick or cake tester comes out clean. Cool completely.
for the frosting
In the bowl of a stand mixer fitted with the whisk attachment, combine cold coconut cream and heavy cream. Whip on medium speed until thickened to soft peaks.
Add vanilla extract and powdered sugar and continue to whip until the cream reaches medium peaks. Keep in refrigerator until ready to frost the cake.
To frost: scoop and spread coconut whipped cream over the entire surface of the cake. Dust with matcha powder and top with toasted coconut if desired.