Preheat oven to 350° F.
To make the crust, first crush up your cookies or crackers in a food processor. You can use a blender, you might have to do it in batches though. Or just put them in a bag and pound them with a rolling pin.
Combine crushed cookies with the melted vegan butter and stir until well combined. You should be able to clump it together easily.
Get a 9" springform pan (you can use 8" or 10" but the filling will be a little taller or shorter) and grease it with cooking spray, though I highly recommend cutting out a circle of parchment paper and lining it with that. I was able to loosen my crust with an offset spatula, but it was kind of a pain in the butt.
Add the cookie mixture to the pan, and using something with a flat bottom (like a glass) lightly press down and even out the crust. Add the pan to the preheated oven for 10 minutes, then remove from oven, and set aside. Lower heat to 325° F.
To make the filling, use the whisk attachment for your stand mixer. Add in the cream cheese, sour cream and lactic acid (if using). Mix on medium speed for 1-2 minutes, and scrape down the sides. Keep mixing until the mixture is smooth and creamy.
Next add in the sugar and salt while the stand mixer is mixing. Add in a bit at a time instead of just dumping it all in at once. Add in the vanilla extract. Scrape down the sides as needed. Next add in the vegan eggs and cornstarch (make a slurry with equal parts water if concerned with lumps though I had no issue). Keep mixing and scraping down sides as needed.
Stop the mixer and then add in the pumpkin puree and pumpkin spice. Mix until well incorporated.
Wrap the bottom of your springform pan in two layers of foil. This is to prevent any water from sneaking in from the water bath. Spray the sides of your springform pan and then add in the filling. Smooth the top with a spatula. Add to a roasting pan and then place in a 325° F preheated oven. Next carefully add some boiling water, enough that it comes up about an inch on your pan.
Bake for 1 hour. After that, leave the cheesecake in the oven for another hour, making sure you don't open the oven door. Some folks leave it open a crack after 20 minutes, but I didn't bother with that. After it's rested in the oven for an hour, remove and let it cool to room temp, then store in the fridge for 6 hours or overnight. Make sure to cover it with some plastic wrap. As the Preppy Kitchen has noted, if you put a paper towel on top, then the plastic wrap, the paper towel will keep the condensation from discoloring the top. But it's optional!
Next, all you need to do is remove from the pan, slice it and serve! I like melting a bit of cookie butter in the microwave and then drizzling that on top, and adding some vegan whip cream!