Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking dish.
In a large bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In another bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the creamed mixture alternately with the coconut milk, mixing until just incorporated.
Fold in the shredded coconut.
Pour the batter into the prepared baking dish and smooth the top.
Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Allow to cool in the baking dish for 10 minutes before transferring to a wire rack to cool completely.