Preheat the oven to 325°F/160°C and grease an 8 x 8-inch square cake pan.
Make the pandan extract: Add the chopped pandan leaves and cold water to a blender and blend on high until the leaves are finely blended. Strain through a fine-mesh sieve, pressing out the liquid and discarding the pulp. Set aside the pandan extract.
Make the egg yolk mixture: In a large mixing bowl, beat the egg yolks and white granulated sugar until pale yellow. Add the melted butter and mix until combined. Add the all-purpose flour and mix just until combined. Do not overmix.
Add the pandan milk: In a separate bowl, whisk together the milk and pandan extract. Microwave for 60 seconds or heat in a small saucepan until lukewarm. Gradually add the warm pandan milk to the egg yolk mixture, about 1⁄4 cup (60 ml) at a time, mixing until combined.
Beat and fold in the egg whites: In a separate mixing bowl, beat the egg whites with an electric hand mixer or stand mixer until stiff peaks form. The peaks should stand upright without drooping when the beaters are lifted. Gently fold the egg whites into the batter with a spatula, one-third at a time, until incorporated. The batter will be very runny and slightly lumpy, which is normal.
Bake the cake: Pour the batter into the prepared cake pan and bake on the middle rack for 60-65 minutes. After 30 minutes, loosely cover the cake with aluminum foil to prevent the top from overbrowning. The cake is done when a toothpick inserted into the center comes out clean. If needed, keep the cake covered and bake for another 10 minutes.
Cool and serve: Let the cake cool in the pan for 10 minutes. Run a knife around the edges of the cake, then carefully transfer it to a wire rack to cool completely before slicing into 12 squares. Dust with icing sugar and serve.