Preheat your oven to 350°F (175°C). Grease and flour a cake pan.
In a mixing bowl, cream the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt. Gradually add to the creamed mixture alternately with coconut milk, beating well after each addition.
Fold in the shredded coconut. Pour the batter into the prepared cake pan.
Bake for 30 minutes or until a toothpick inserted into the center comes out clean. Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.