Preheat oven to 375°F. Grease an 8x8 inch pan with cooking spray.
Homogenize Coconut Milk: Open the can of coconut milk and thoroughly combine the contents (the heavy fat must be blended with the liquid). Use a blender, food processor, or stand mixer until the consistency is similar to cream.
Combine Wet Ingredients: In a large bowl, stir together the homogenized coconut milk, melted coconut oil, eggs, granulated sugar, and vanilla extract.
Combine Dry Ingredients: In a medium bowl, whisk together the flour, shredded coconut, and baking powder.
Finish Batter: Add the dry ingredients to the wet ingredients. Mix until just combined (do not overmix).
Bake: Pour the batter into the prepared pan and bake for 30-40 minutes until the top is golden brown and a toothpick inserted in the center comes out clean.
Cool: Remove the cake from the oven and allow it to cool completely in the pan on a wire rack.
Finish: When cooled, the top of the cake can be sprinkled with powdered sugar (optional).
Store: Wrapped well or stored in an airtight container at room temperature, the cake remains fresh for up to 1 week.