Preheat the oven to 350 degrees F and line an 8 x 8-inch baking dish with parchment paper.
Mix 1/2 of a can of pumpkin puree, 1/2 cup vegan cream cheese, 1/2 cup brown sugar, 2 1/2 tbsp corn starch, 1 tsp vanilla, 1 tsp lemon juice, and 1/2 tsp pumpkin spice. Blend until smooth and creamy and set aside. (I like to put it in a bowl and use an immersion blender, but you can also use a regular blender or food processor.)
Pour the remaining 1/2 can of pumpkin puree into a mixing bowl with 3/4 cup sugar, 1/3 cup oil, and 1 tsp vanilla then mix well.
Add 1 cup flour, 1/3 cup cocoa powder, 1/2 tsp baking soda, and1/4 tsp salt and mix until it's well incorporated.
Pour 1/2 of the chocolate brownie batter into the bottom of the baking dish.
Then pour all of the pumpkin cheesecake batter on top of it.
Finally, drop spoonfuls of the remaining brownie batter on the top of the pumpkin layer and use a knife to make swirls on the top.
Bake at 350 degrees F for 30 minutes until the top is dry and shiny.
Allow cooling completely before pulling the brownies out of the pan and cutting with a large knife on a flat surface.
Notes
Don't over-mix the brownie batter, just stir it until all of the flour is mixed in and there are no dry spots left.
Bake for the full 30 minutes until the top is shiny, dry, and starting to form small cracks.
For perfect-looking brownies, use a large knife and cut down straight and firmly, whipping the knife between each cut.
You can also leave out the pumpkin swirl and simply bake the pumpkin brownie batter as is.
Allow them to cool completely before cutting. The pumpkin cheesecake filling needs to cool to set up and be firm.