Preheat the oven to 375 degrees F. Grease a 13 by 18 by 1-inch sheet pan. Line the pan with parchment paper and grease and flour the paper.
In a small bowl, sift together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt and stir to combine. Place the eggs and granulated sugar in the bowl of an electric mixer fitted with the paddle attachment and beat on medium-high speed for 3 minutes, until light yellow and thickened. With the mixer on low, add the pumpkin, then slowly add the flour mixture, mixing just until incorporated. Finish mixing the batter by hand with a rubber spatula. Pour into the prepared pan and spread evenly. Bake the cake for 10 to 12 minutes, until the top springs back when gently touched.
While the cake is baking, lay out a clean, thin cotton dish towel on a flat surface and sift the entire 1/4 cup of confectioners' sugar evenly over it. (This will prevent the cake from sticking to the towel.) As soon as you remove the cake from the oven, loosen it around the edges and invert it squarely onto the prepared towel. Peel away the parchment paper. With a light touch, roll the warm cake and the towel together (don't press!) starting at the short end of the cake. Allow to cool completely on a wire rack.
Meanwhile, make the filling. In the bowl of an electric mixer fitted with the paddle attachment, beat the mascarpone, confectioners' sugar, and cream together for about a minute, until light and fluffy. Stir in the crystallized ginger, and salt.
To assemble, carefully unroll the cake onto a board with the towel underneath. Spread the cake evenly with the filling. Reroll the cake in a spiral using the towel as a guide. Remove the towel and trim the ends to make a neat edge. Dust with confectioners' sugar and serve sliced.