Preheat oven to 350 degrees. Grease and line a 9X4.5-inch loaf pan (or equivalent) and set aside.
Sift together the dry ingredients and set aside.
In the bowl of an electric mixer fitted with a paddle attachment, place the butter and coconut oil. With the mixer on medium, mix until combined. Add the sugar and mix on medium for about 3-5 minutes, or until creamed.
Add in the vanilla and eggs, mixing well in between. Stop the mixer and scrape down the sides and bottom of the bowl.
With the mixer on low and working in alternating batches, add in the flour mixture and coconut milk - starting and ending with the flour mixture.
Mix on medium for no more than 30 seconds or until combined.
Pour batter into the prepared loaf pan and bake for 40 to 50 minutes, or until a toothpick inserted in to the center of the cake comes out clean.
Let cool on a wire rack for 15 minutes before removing cake from its pan.
For the frosting, mix the butter with electric beaters until creamy
Carefully add in the confectioner's sugar, coconut milk, and vanilla until combined.
Mix on medium until frosting until fluffy, 2 to 3 more minutes.
After the cake has completely cooled, swirl on the coconut frosting and use a mesh sieve to dust with matcha powder, if desired.