Prepare the caramel:
In a small saucepan, combine sugar and water over medium heat. Stir occasionally until the sugar melts and turns golden brown (about 5 minutes). Be careful not to burn the sugar. Once caramelized, carefully pour the hot caramel into a round or fluted baking dish (approximately 8-inch size), swirling to coat the bottom evenly. Let the caramel cool and harden while you prepare the pudding.

Make the pudding mixture:
In a blender, combine coconut milk, sweetened condensed milk, whole milk, eggs, shredded coconut, and vanilla extract (if using). Blend on medium speed for about 30 seconds until the mixture is smooth and well combined.

Bake the pudding:
Pour the pudding mixture into the caramel-coated baking dish. Place the dish in a large baking pan and fill the outer pan with hot water until it reaches halfway up the sides of the pudding dish (this is called a water bath).
Carefully transfer the pan to the oven and bake at 350°F (175°C) for 45–50 minutes, or until the pudding is set. You can test for doneness by gently shaking the dish—if the center wobbles slightly, it’s done.

Cool and chill:
Remove the pudding from the water bath and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours, or preferably overnight, to allow the flavors to develop and the texture to set.

Serve:
To serve, run a knife around the edges of the pudding to loosen it. Place a plate over the dish and flip it upside down. Gently lift the dish to reveal the beautiful caramel top. Slice and serve chilled.