Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking dish or line it with parchment paper for easy removal.
In a large mixing bowl, combine the pumpkin puree, granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract. Mix until smooth and well combined.
In another bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, ginger, and salt. Gradually add the dry ingredients to the wet mixture, gently folding until just combined; do not overmix.
In a separate mixing bowl, beat the softened cream cheese with the granulated sugar until smooth and creamy. Add in the egg and vanilla extract, mixing again until well combined.
Pour about two-thirds of the pumpkin batter into the prepared baking dish and spread it evenly. Spoon dollops of the cream cheese mixture over the pumpkin layer. Then, add the remaining pumpkin batter on top.
Using a knife or a skewer, gently swirl the cream cheese mixture into the pumpkin batter to create a marbled effect. Be careful not to fully mix them; you want a beautiful swirl.
Place the baking dish in the preheated oven and bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Once baked, take the bars out of the oven and let them cool in the pan for about 10 minutes. Then, transfer to a wire rack to cool completely. Once cooled, cut into squares and serve.
For an extra touch, drizzle with a simple icing made from powdered sugar and milk or sprinkle with a bit of cinnamon before serving.