Place a 21cm/8-inch flanera or similar-sized cake pan on a tray and set aside. If using a cake pan, make sure that it does NOT have a removable base.
Caramel: Add the sugar and water to a saucepan and place it over low heat. Stir the mixture with a spoon for several minutes until all of the sugar has dissolved.Turn up the heat to medium-high and DO NOT TOUCH OR STIR IT from this point on. Keep a very close eye on the saucepan, the mixture will start to boil and bubble. After several minutes it will start to turn a light caramel color in places. Very gently swirl the pan so that it caramelizes evenly. Once the caramel turns a deep amber color, remove it from the heat.
Pour the caramel into the flanera or cake pan, working quickly as it will set very fast. Allow the caramel to come to room temperature and harden (about 30 minutes).
Custard: Add the evaporated coconut milk, condensed coconut milk, non-dairy milk, cream cheese, cornstarch, agar-agar, vanilla, and salt to a high-speed blender and blend until smooth.
Pour the custard mixture into a saucepan and place it over medium heat. Bring the mixture to a simmer, while continuously whisking. Continue to simmer for 5 minutes, the custard will start to thicken. Make sure you are constantly stirring the custard to avoid it burning to the bottom of the pan. I recommend alternating between a whisk and a rubber spatula. Remove from the heat.
Place the cubed butter into a large mixing bowl and sit a fine-mesh sieve on top of the bowl. Pass the custard through the sieve into the bowl with the butter and whisk the butter through until smooth and creamy. Allow it to cool at room temperature for 20 minutes. Every 5 minutes, whisk the custard to prevent a skin from forming on top of it.
Pour the custard on top of the set caramel and smooth out the top using the back of a spoon or an offset spatula. Let it continue to cool to room temperature, then cover with clingfilm before placing them in the fridge. Refrigerate for 12-24 hours.
Serving: Just before serving,
Place a large serving plate on top of the pan and quickly turn it over. Very slowly start to lift the pan. The custard will unmold itself and the caramel sauce will pour down the sides of the flan.
Storage: This flan is best served within the first 1-2 days once it has set. Do not remove it from the mold until just before serving. I recommend making it one day ahead of serving.
