Preheat your oven to 375°F (190°C). Line a jelly roll pan (10x15 inch) with parchment paper and lightly grease it.

In a medium bowl, whisk together the flour, baking powder, baking soda, pumpkin pie spice, and salt.

In a separate larger bowl, beat the eggs and granulated sugar until light and pale. Then add the pumpkin purée and vanilla extract. Stir until smooth.

Pour the dry ingredients into the wet ingredients and gently fold everything together until just combined.

Spread the batter evenly into the prepared pan and bake for 13 to 15 minutes, or until the top springs back when touched lightly.

While the cake is still warm, dust a clean kitchen towel with powdered sugar. Flip the cake onto the towel, peel off the parchment paper, and roll it up gently starting from the short end. Let it cool completely.

To make the filling, beat together the cream cheese and butter until creamy. Add the powdered sugar and vanilla and beat until fluffy.

Once the cake is fully cooled, unroll it gently, spread the cream cheese filling evenly, and roll it up again. Wrap in plastic wrap and chill for at least an hour before slicing.