Preheat the oven to 375°F (190°C).
Prepare a 15x10-inch jelly roll pan by greasing it and lining it with parchment paper.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
In another large bowl, mix the eggs and granulated sugar using an electric mixer until pale and thick.
Add pumpkin puree and pumpkin spice to the egg mixture and beat until well combined.
Gently fold the dry ingredients into the wet mixture until just combined, taking care not to overmix.
Pour the batter into the prepared pan and spread it out evenly, then bake for 12-15 minutes.
Once baked, remove the cake from the oven and immediately invert it onto a clean kitchen towel that has been dusted with powdered sugar.
Peel off the parchment paper and carefully roll the cake with the towel, starting from one of the short ends.
Let the rolled cake cool completely at room temperature.
Prepare the filling by beating together the cream cheese, powdered sugar, vanilla extract, and heavy cream until smooth.
Once the cake is cool, carefully unroll it and spread the cream cheese filling over the surface evenly.
Re-roll the cake gently and wrap it in plastic wrap, then refrigerate for at least 1 hour to set.
Slice and serve garnished with additional powdered sugar or whipped cream, if desired.