Preheat the oven to 350°F and lightly grease a 9-inch springform pan.
In a medium bowl, mix together the cookie crumbs and sugar. Drizzle in the melted coconut oil and vegan milk and stir with a fork until the crumbs are evenly moistened.
Press the mixture firmly into the bottom of the pan in an even layer. Bake for 10 minutes, then transfer the pan to a cooling rack. Leave the oven on.
Drain the cashews and let cool to room temp if you boiled them. Add them to a high-speed blender along with the tofu, raspberries, sugar, apple cider vinegar, lemon juice, melted coconut oil, cornstarch, vanilla, salt, and citric acid, if using.
Puree until completely smooth, scraping down the sides as needed. This can take 3 to 5 minutes depending on your machine. The smoother the better.
Pour the filling over the baked crust and smooth the top with a rubber spatula.
Bake for 55 to 60 minutes, until the top is lightly puffed and the edges are starting to pull away from the pan. The top will look darker than the inside of the cheesecake, slightly browned in spots even. That is normal.
Set the pan on a wire rack to cool while you make the topping.
About 20 minutes before the cheesecake is fully baked, start the topping. Mix the cornstarch with the cold water and lemon juice to make a slurry, making sure no big lumps are left. Combine with the raspberries and sugar in a small saucepan. Place over medium heat and bring to a boil, stirring often. The raspberries will begin to burst.
Lower the heat to a simmer and cook for about 5 more minutes, until thickened. Let sit for about 5 minutes, just until it isn't steaming.
Pour the warm topping over the warm cheesecake. Refrigerate to set for at least 4 hours, though overnight is best. Wrap with plastic wrap once it's cool enough to handle.
To cut, release the springform and slice with a sharp knife dipped in cold water for clean cuts. Serve with whipped topping and fresh raspberries, if you like!
