Preheat your oven to 350°F (175°C) and grease two 9-inch round cake pans.
In a large mixing bowl, cream the softened butter and sugar until fluffy.
Add the eggs one at a time, mixing well after each addition.
Stir in the coconut milk and vanilla extract until well combined.
In another bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the shredded coconut gently into the batter.
Divide the batter evenly between the prepared pans.
Bake for 30-35 minutes, or until a toothpick inserted comes out clean.
Let the cakes cool in the pans for 10 minutes before transferring to wire racks to cool completely.