In a small saucepan combine the 1/2 cup sugar until with 2 tablespoons water and heat until the sugar is completely dissolved and it turns a golden brown color. Carefully pour the caramelized sugar into the bottom of a 10-inch cake pan. Tilt the pan, from side to side, in a circular motion swirling the sugar around so that evenly coats the bottom of the pan.
Place the cake pan into a baking dish large enough to accommodate the cake pan and set aside to cool. The sugar will harden as it cools.
In a large mixing bowl combine eggs, egg yolks, salt, vanilla, remaining 2/3cup sugar and coconut milk.
Whisk until well blended.
Pour custard mixture into the cake pan over the caramelized sugar.
Place the flan into the oven and pour warm water into the baking dish so that it comes up about 1 1/2-inches up the side of the cake pan.
Bake at 325 degrees F for 1 hour or until knife inserted near center comes out clean.
Remove from the oven and let cool to room temperature. Chill for at least 1 hour or overnight in the refrigerator. To unmold the flan, run a knife around the edge of the cake pan and invert onto a plate.
Preheat oven to 400 degrees F and line 2 baking sheets with parchment paper.
In a medium bowl, sift together the flour, sugar, and salt. Beat in the egg whites and melted butter until well incorporated.
Spoon out batter, about 1/2 a tablespoon at a time, onto a parchment lined baking sheets.
Spread cookies into 2 to 3 inch circles about 1/8-inch thick.
Sprinkle with coconut and bake 6 minutes or until slightly browned. Allow to cool completely on the baking sheets. Carefully peel from parchment and serve with coconut flan.
