Line an 8x8-inch baking pan with parchment paper, leaving overhang on two sides. In a medium bowl, combine graham cracker crumbs and sugar, then stir in melted butter until the mixture resembles wet sand.
Press the crumb mixture firmly into the bottom of the prepared pan using the back of a measuring cup. Bake at 350°F for 8-10 minutes until lightly golden and set. Remove and let cool slightly.
In a large mixing bowl, beat softened cream cheese on medium speed until smooth, about 1 minute. Gradually add sugar and beat until incorporated, scraping down the sides as needed.
Add eggs one at a time, mixing on low speed just until combined after each addition. Stir in vanilla extract. Avoid overbeating to prevent air bubbles. Pour over the cooled crust and spread evenly.
In a separate medium bowl, whisk together pumpkin puree and sugar. Add egg and whisk until smooth. Incorporate cinnamon, nutmeg, and optional ginger, mixing thoroughly without lumps.
Gently spoon the pumpkin mixture over the cheesecake layer. Use a butter knife or skewer to swirl the layers lightly for a marbled effect, being careful not to disturb the crust.
Bake at 350°F for 35-45 minutes until the center is set but slightly jiggly and edges are lightly browned. Check at 35 minutes; a toothpick inserted in the center should come out mostly clean.
Turn off the oven and crack the door, allowing bars to cool inside for 30 minutes to prevent cracking. Transfer to a wire rack to cool completely at room temperature, about 1 hour.
Cover the cooled pan with plastic wrap and refrigerate for at least 4 hours or overnight for clean slices. Use parchment overhang to lift bars from pan.
Cut into 16 squares with a sharp knife, wiping the blade between cuts. Serve chilled for best texture.