Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch cake pan.

Beat sugar, butter, and egg yolks together in a bowl using an electric mixer until smooth and creamy; add shredded coconut.

Whisk flour, baking powder, and salt together in a bowl. Stir creamed butter mixture, alternating with coconut milk, into flour mixture until batter is just mixed.

Beat egg whites in a glass or metal bowl until soft peaks form. Fold egg whites into batter. Pour batter into the prepared cake pan.

Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 45 minutes.