In a mixing bowl, combine graham cracker crumbs, shredded coconut, brown sugar, and melted butter until well integrated. Press firmly into a greased square pan to create an even layer.

In a medium saucepan, whisk together condensed milk, coconut milk, whole milk, and cornstarch over medium heat, stirring continuously for 5-6 minutes until thickened.

Remove from heat and stir in butter, vanilla extract, and white rum until smooth. Allow to cool for 5 minutes before pouring over the crust.

Let the squares cool at room temperature for 20 minutes, then refrigerate for at least 4 hours until set.

Once set, remove from the pan, slice into squares, and sprinkle toasted coconut on top before serving.