In a medium bowl, combine graham cracker crumbs, shredded coconut, brown sugar, and melted butter, mixing until fully incorporated. Press this mixture into the bottom of a lined 8x8-inch pan and refrigerate to chill.

In a saucepan over medium heat, whisk together cornstarch, full-fat coconut milk, condensed milk, and whole milk. Continuously stir until it thickens to a pudding-like consistency, about 8-10 minutes.

Remove from heat and stir in the butter, shredded coconut, and vanilla extract until fully dissolved. Allow to cool for about 5 minutes before mixing in the white rum.

Pour the custard filling over the chilled crust, spreading it evenly. Ensure it reaches the edges and is level.

Let sit at room temperature for about 20 minutes, then refrigerate for at least 4 hours until set.

Once set, slice into squares and sprinkle toasted coconut on top before serving.