Preheat the oven to 350°F and line an 8-inch by 8-inch baking dish with parchment paper.
Mix 1/2 can of pumpkin puree, 1/2 cup vegan cream cheese, 1/2 cup brown sugar, 2 1/2 tbsp cornstarch, 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, and 1/4 tsp salt, and mix until well incorporated.
Pour 1/2 of the chocolate brownie batter into the bottom of the baking dish.
Then pour all the pumpkin cheesecake batter over it.
Finally, drop spoonfuls of the remaining brownie batter onto the pumpkin layer and use a knife to swirl the top.
Bake at 350°F for 30 minutes, until the top is dry and shiny.
Let the brownies cool completely before pulling them out of the pan and cutting them with a large knife on a flat surface.
Notes
Don't overmix the brownie batter; stir only until the flour is combined and no dry spots remain.
For more chocolaty brownies, add 3/4 cup of chocolate chips to the brownie batter.
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 straight down firmly, wiping the knife between each cut.
You can also leave out the pumpkin swirl and simply bake the pumpkin brownie batter as is.
Allow the vegan pumpkin brownies to cool completely before cutting. The pumpkin cheesecake filling needs to cool to set and firm up.