Cookbook author Odette Williams serves this cake for breakfast, and her family loves it.
Arrange a rack in the center of the oven; preheat to 350°. Grease an 8-inch round cake pan with 2-inch-high sides with butter. Line the bottom and sides of the pan with parchment paper, then grease the paper. (Alternatively, skip the parchment and grease the pan. Dust the pan with 1/3 cup shredded coconut. Tap any excess coconut out of the pan.)
Sift the flour, baking powder, and salt into a large bowl. Whisk in 1 cup shredded coconut and the sugar. In a small bowl, whisk the coconut milk and eggs. Gradually stir the wet ingredients into the dry ingredients just until blended. Stir in the melted butter.
Pour the batter into the prepared pan and smooth the top. Bake until a tester inserted into the center of the cake comes out clean and the cake bounces back when pressed lightly, 30 to 35 minutes. Let cool for 10 minutes.
Run a butter knife around the sides of the pan. Invert the cake onto a wire rack and remove the parchment. Turn the cake right-side up and let cool on the rack. Dust with confectioners’ sugar.