1. Preheat your oven to 350°F and line a 9×9-inch baking pan with parchment paper.

2. In a bowl, combine the graham cracker crumbs, melted butter, and sugar until the mixture resembles wet sand. Press this mixture firmly into the bottom of the prepared pan and bake for 10 minutes. Allow the crust to cool completely.

3. In a mixing bowl, beat the softened cream cheese and sugar until smooth and creamy. Add the eggs one at a time, mixing just until incorporated after each addition, then blend in the vanilla extract.

4. Spread about half of the cheesecake mixture evenly over the cooled crust.

5. In a separate bowl, whisk together the pumpkin puree, pumpkin pie spice, and brown sugar until smooth. Gently fold this pumpkin mixture into the remaining cheesecake batter.

6. Dollop the pumpkin-cheesecake mixture over the first layer. Use a butter knife to gently swirl through both layers. Bake for 35-40 minutes, until the edges are set but the center still has a slight jiggle.

7. Allow to cool completely in the pan, then refrigerate for at least 2 hours before slicing.