Preheat the oven to 350°F (180°C). Grease and flour two 8-inch round cake pans.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, beat the butter and sugar with an electric mixer until light and fluffy. Add the eggs one at a time, beating well after each addition. Beat in the vanilla extract.
Gradually add the dry ingredients to the butter mixture, alternating with the coconut milk. Mix until just combined. Stir in the shredded coconut.
Divide the batter evenly between the prepared pans. Bake for 25-30 minutes or until a toothpick inserted in the center of the cake comes out clean.
Let the cakes cool in the pans for 10 minutes, then remove them from the pans and transfer them to a wire rack to cool completely.