Place the raw cashews and the coconut milk in a food processor. Feel free to use the same one you used for the crust. Pulse the food processor for several seconds to break down the cashews. Open the lid and stir down any ingredients that might have risen to the top of the bowl. Now pulse for several seconds, up to a minute, until smooth and creamy.
Add the vegan cream cheese and pulse again until smooth and creamy.
Next, add the sugar, corn starch, flour, and vanilla. Pulse for several seconds, up to a minute, until you have a nice, creamy mixture.
Preheat your oven to 350°F while the filling settles for a few minutes.
When the oven is ready, pour the cheesecake filling into the prepared crust.
Wrap the bottom of the pan in aluminum foil, being sure to cover the bottom half of the pan. Place this in a roasting pan and pour hot water around the bottom of the pan. This is a water bath and it will prevent the cheesecake from cracking in the middle.
Bake the cheesecake for 60 minutes and then turn the oven off and leave the cheesecake in the oven for up to another hour (or until it's cooled). Remove from the oven and allow it to cool before placing it in the fridge. I recommend refrigerating the cheesecake for at least four hours (or even a full day) before slicing and serving.