Preheat oven to 375 degrees. Line a 10 x 15-inch jelly roll pan with parchment paper, prepare the paper with nonstick cooking spray, and set aside.
In a small bowl, whisk together the flour, baking powder, baking soda, pumpkin pie spice, and salt. In a large bowl, combine the sugar and eggs and beat until thickened, about 2 minutes.
Add the pumpkin and mix to combine. Fold in the flour mixture until combined. Spread the batter evenly into the bottom of the prepared pan. Bake for 13–15 minutes, until the top of the cake springs back when lightly pressed.
Remove cake from oven, run a spatula around the sides of the pan to loosen, and turn it out onto a clean dish towel; peel off parchment paper. Starting with the shorter end, carefully roll up the cake with the towel and place seam-side down on a wire rack; cool to room temperature.
In a medium bowl, combine the cream cheese and butter and beat until smooth. Add the powdered sugar and vanilla and beat until smooth. Carefully unroll the cake and spread evenly with cream cheese filling.
Re-roll the cake, wrap in aluminum foil, and refrigerate for at least 1 hour. To serve, sprinkle cake with powdered sugar and cut into 1 1⁄4-inch slices.