Preheat the oven to 375°F (190°C). Line a 15x10-inch jelly-roll pan with parchment paper, leaving a little overhang, and lightly grease the parchment.
Whisk the dry ingredients: in a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt.
Beat the eggs and sugar: in a large bowl, beat the eggs and granulated sugar with an electric mixer on high for 2 to 3 minutes, until thick, pale, and ribbons off the beaters.
Add the pumpkin: beat in the pumpkin puree and vanilla on low just until combined.
Fold in the flour: sprinkle the dry ingredients over the batter and fold gently with a spatula just until no flour streaks remain. Do not overmix.
Bake: spread the batter evenly into the prepared pan, right into the corners. Bake for 13 to 15 minutes, until the top springs back when lightly touched and a toothpick comes out clean.
Roll it warm: while the cake bakes, lay a clean thin kitchen towel on the counter and dust it generously with powdered sugar. As soon as the cake comes out of the oven, flip it onto the towel, peel off the parchment, and — starting from a short end — roll the cake up inside the towel. Let it cool completely in the towel, about 1 hour. This trains the sponge so it will not crack later.
Make the filling: beat the cream cheese, powdered sugar, butter, and vanilla together until completely smooth and fluffy, 2 to 3 minutes.
Fill and re-roll: carefully unroll the cooled cake, spread the filling evenly over it, leaving a 1/2-inch border, and re-roll it snugly (without the towel this time). Wrap tightly in plastic wrap.
Chill and slice: refrigerate for at least 1 hour, or up to 2 days, so the filling sets for clean slices. Dust with powdered sugar, slice with a sharp serrated knife, wiping the blade between cuts, and serve.