Makes one 9x1''/23x2.5cm tart pan with removable bottom.
Lightly toast the shredded coconut and save some for the topping. Warm up coconut milk (just warm) with vanilla, rum and mix in the toasted coconut. Set aside a couple of hours allowing the coconut to absorb the liquid, or refrigerate overnight. In a separate bowl, combine together the yolks, the egg, sugar, starch, and salt. Incorporate in the coconut-milk mixture.
Grease the tart pan with cooking spray or softened butter and flour. Mix all ingredients together. Using a spoon, spread the coconut mixture evenly into the bottom of the tart pan and all the way up to the sides. Fill with the coconut custard and bake.
Set the oven rack adjusted to the middle position with a baking sheet or a pizza stone; this will allow the pie to get a nice browned bottom. Bake in a preheated 350ºF/180ºC oven for about 30 minutes. Remove from the oven and let cool completely, and chill prior un-molding. Top pie with the saved toasted coconut. Enjoy!