Preheat the oven to 375°F (190°C). Grease a 10x15-inch jelly roll pan and line it with waxed paper.

In a medium bowl, whisk together flour, cinnamon, baking powder, ginger, nutmeg, and salt until evenly combined.

In a large bowl, beat sugar and eggs with an electric mixer until pale and well blended. Mix in the pumpkin puree, then fold in the flour mixture until just incorporated. Pour the batter into the prepared pan and smooth the top.

Bake until the cake springs back when touched and a toothpick inserted in the center comes out clean, about 15 minutes. Set the pan on a wire rack and let cool for 10 minutes.

Turn the cake out onto a clean kitchen towel. Peel off and discard the waxed paper. Starting at a short end, roll the cake and towel together into a log and let cool completely, about 30 minutes.

For the filling, beat cream cheese, confectioners' sugar, butter, remaining 1 tablespoon pumpkin puree, and vanilla in a mixing bowl until smooth and creamy.

Place a large sheet of plastic wrap on a work surface. Unroll the cooled cake carefully and lay it on the plastic wrap. Spread the filling evenly over the cake.

Roll the cake back into a log, using the plastic wrap to help, and wrap it tightly. Put the roll seam-side down on a plate and refrigerate until fully chilled, about 2 hours.