Line an approximately 8x5-inch rectangular container with parchment paper.
In a saucepan, combine half of the coconut milk and the sugar.
Add the cornstarch to the remaining coconut milk in the can and whisk it together until smooth.
Warm the coconut milk and sugar mixture in the saucepan over low heat, stirring to dissolve the sugar.
Slowly pour in the cornstarch-coconut milk mixture while whisking constantly.
Continue to whisk over low heat until the mixture is thick and pasty, about 3 to 4 minutes.
Pour the mixture into the parchment-lined container and let it cool to room temperature.
Transfer to the fridge and chill until fully set, at least 2 hours.
Use the parchment sling to transfer the pudding to a cutting board and cut into bite-sized cubes.
Roll in the shredded coconut just before serving and enjoy cold.
