Preheat your oven to 350°F (175°C).
In a medium bowl, whisk the egg whites and granulated sugar together until well combined.
Gradually stir in the coconut milk, shredded coconut, glutinous rice flour, and vanilla extract. Mix thoroughly, ensuring the batter is smooth with no lumps of coconut. The mixture will have a thin, liquid consistency.
Pour the batter into a greased 8×8-inch baking pan. Bake in the preheated oven for 45 minutes, or until the cake is set and slightly golden.
Carefully remove the cake from the oven. Brush the beaten egg yolks evenly over the top of the cake.
Set your oven to broil and return the cake to the oven for 5-10 minutes. Watch it closely as it will brown quickly. Remove once the top is golden brown.
Cool the cake completely on a wire rack. Once cooled, cover the cake with plastic wrap and refrigerate for at least 8 hours (or overnight) to allow it to set.
Cut the cake into squares or triangles and serve chilled or at room temperature.