Preheat the oven to 375°F. Line a 10x15-inch jelly roll pan with parchment paper and lightly grease the paper.
In a large bowl, beat the eggs and granulated sugar until light and fluffy. Mix in the pumpkin puree and vanilla extract.
In a separate bowl, whisk together the flour, baking powder, pumpkin pie spice, baking soda, and salt.
Gradually add the dry ingredients to the pumpkin mixture and stir until just combined.
Spread the batter evenly into the prepared pan and bake for 12 to 15 minutes, or until the cake springs back when touched.
While the cake bakes, spread a clean kitchen towel on the counter and dust it generously with powdered sugar.
Turn the warm cake onto the prepared towel. Carefully remove the parchment paper and roll the cake up with the towel starting from the short end.
Allow the rolled cake to cool completely.
To make the filling, beat together the cream cheese, butter, powdered sugar, and vanilla extract until smooth and creamy.
Carefully unroll the cooled cake and spread the filling evenly over the surface, leaving a small border around the edges.
Roll the cake back up without the towel and wrap tightly in plastic wrap.
Refrigerate for at least 1 hour before slicing.
Dust with additional powdered sugar if desired, then slice and serve.