Heat the oven to 375 degrees F. Butter a 10x15-inch jelly roll pan and line the bottom with waxed paper.

Whisk together the flour, cinnamon, baking powder, ginger, nutmeg, and salt in a medium bowl.

In a large bowl, beat the sugar and eggs with an electric mixer until well blended. Mix in the 2/3 cup pumpkin puree, then stir in the flour mixture until just combined. Pour the batter into the prepared pan and spread it evenly.

Bake until a toothpick inserted in the center comes out clean, about 15 minutes. Cool the cake in the pan on a wire rack for 10 minutes.

Turn the cake out onto a clean kitchen towel and peel off the waxed paper. Starting with a short end, roll the cake and towel together into a log. Cool completely, about 30 minutes.

In a separate bowl, beat the softened cream cheese, powdered sugar, butter, the remaining 1 tablespoon pumpkin puree, and vanilla until the mixture is silky smooth.

Cover your work surface with a large sheet of plastic wrap. Gently unroll the cooled cake and set it on the plastic wrap.

Evenly spread the cream cheese filling over the cake, then roll it up again without the towel, using the plastic wrap to help guide it. Wrap securely, place the roll seam side down on a plate, and refrigerate until fully chilled, about 2 hours.