Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch pan.
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.
Combine flour, baking powder, and salt; gradually add to the creamed mixture alternating with the coconut milk.
Pour the batter into the prepared pan.
Bake for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Allow cake to cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.