Heat the oven to 350°F (175°C). Line an 8×8-inch pan with parchment or grease it lightly.

In a medium bowl, whisk the egg whites together with the sugar until they’re well combined and slightly glossy.

Pour in the coconut milk, then fold in the shredded coconut, glutinous rice flour, and vanilla. Mix until everything is smooth and there are no dry pockets of flour or clumps of coconut. The batter will be quite loose — that’s normal.

Transfer the mixture to the prepared pan and smooth the surface with a spatula. Bake on the center rack for about 45 minutes, until the top looks set and the edges begin to brown.

Remove the pan and gently brush the surface with the reserved egg yolks. Switch the oven to broil and return the pan to the top rack. Broil briefly (about 5–10 minutes) until the top turns a golden brown — watch it closely so it doesn’t burn. Bold tip: Keep the oven door slightly ajar and stay nearby — broilers brown fast.

Cool the pan on a wire rack until it reaches room temperature. Cover with plastic wrap and refrigerate overnight (or ~8 hours) so the cake firms up and slices cleanly.

Cut into squares or triangles and serve straight from the fridge or at room temperature.