Preheat oven to 350°F (175°C).Grease a 9x13-inch cake pan.
In a large mixing bowl, beat the sugar, butter, and egg yolks together using an electric mixer until smooth and creamy. Add the shredded coconut and mix well.
In another bowl, whisk together the flour, baking powder, and salt.
Slowly stir the creamed mixture into the flour mixture, alternating with the coconut milk, until the batter is just mixed.
Bake in the preheated oven for approximately 45 minutes or until a toothpick inserted into the center of the cake comes out clean.