Preheat oven to 350°F (175°C).
Line a 9×13-inch pan with parchment paper.
Whisk pumpkin puree, eggs, brown sugar, granulated sugar, oil, and vanilla until smooth.
In a separate bowl, whisk flour, baking powder, salt, cinnamon, nutmeg, and ginger.
Fold the dry ingredients into the pumpkin mixture until just combined.
Beat softened cream cheese, sugar, egg, and vanilla until smooth.
Spread the pumpkin batter evenly in the prepared pan.
Drop spoonfuls of cream cheese mixture over the pumpkin batter.
Swirl gently with a knife using about 4–5 figure-eight passes.
Bake for 35–40 minutes, until the center has a slight jiggle and a toothpick comes out with moist crumbs.
Cool in the pan for at least 2 hours.
Slice and serve.