Preheat oven to 350F and prepare three 6-inch cake pans.
In the bowl of a standing mixer, cream together butter and granulated sugar until pale and fluffy. Add eggs one at a time and mix well.
In a medium-sized bowl, whisk together flour, baking powder, salt, and shredded coconut.
Combine coconut milk and milk in a separate cup.
Alternating between the milk and dry ingredients, gradually incorporate the two to the butter-sugar mixture. Careful not to overmix.
Transfer batter into the prepared cake pan. Bake for 28 - 30 minutes, or until an inserted toothpick comes out clean.
Coconut White Miso Buttercream
With a mixer, beat the butter and icing sugar until pale and fluffy.
Add the coconut milk and mix well.
Add the white miso, one teaspoon at a time. Taste the buttercream as you go along. You can add more or less miso depending on how much of a subtle savoury note you would like.