Preheat the oven to 350°F (175°C) and line an 8x8 inch square baking pan with parchment paper.
In a large mixing bowl, whisk together the melted coconut oil, 1 cup sugar, applesauce, and 1 teaspoon vanilla extract until smooth.
Sift in the flour, cocoa powder, and salt. Stir until just combined, ensuring no dry streaks remain.
Reserve 1/4 cup of the brownie batter and spread the remaining batter evenly into the bottom of the prepared baking pan.
In a separate medium bowl, beat the vegan cream cheese, pumpkin puree, 1/3 cup sugar, cornstarch, pumpkin pie spice, and 1/2 teaspoon vanilla extract until creamy and smooth.
Carefully spread the pumpkin cheesecake mixture over the brownie layer in the pan.
Dollop the reserved brownie batter over the pumpkin layer and use a toothpick or knife to gently swirl the two layers together.
Bake for 35 to 40 minutes, or until the edges are firm and a toothpick inserted into the center comes out with only a few moist crumbs.
Remove from the oven and allow to cool completely in the pan at room temperature, then refrigerate for at least 2 hours before slicing to allow the cheesecake layer to set.