Preheat your oven to 375 degrees Fahrenheit and grease a 15-by-10-inch jelly roll pan thoroughly.
Line the bottom of the pan with parchment paper to ensure the cake releases cleanly.
Whisk the flour, baking powder, pumpkin pie spice, and salt in a medium bowl until fully combined.
Beat the eggs in a large mixing bowl until thick and lemon-colored to incorporate air.
Fold the pumpkin puree into the egg mixture until the batter is a uniform color.
Gradually fold in the dry ingredients until just combined.
Spread the batter evenly into the prepared pan and bake for 15 minutes.
While the cake is still warm, turn it onto a clean kitchen towel dusted with powdered sugar.
Carefully peel off the parchment paper and roll the warm cake tightly with the towel.
Allow the rolled cake to cool completely on a wire rack.
While cooling, beat the softened cream cheese, powdered sugar, and softened butter until smooth.
Unroll the cooled cake, spread the filling evenly, and roll it back up without the towel.
Dust with additional powdered sugar if desired before serving.