Adjust oven rack to the middle rack. Heat the oven to 325°F. Spray a 18- by 13-inch rimmed baking sheet with nonstick cooking spray. Line with parchment paper. Spray the parchment paper. Set aside.
Whisk the flour, ginger, baking soda, and salt in medium bowl; set aside. In the bowl of an electric mixer fitted with a whisk attachment beat the eggs and sugar on medium high until pale yellow and thick, about 5 minutes.
Sift the flour mixture over the egg foam. Fold until combined, making sure to scrape the sides and bottom of the bowl. Pour the batter into the prepared pan and spread to an even thickness with the spatula. Bake until cake is firm and springs back when touched, about 18 minutes. Before cooling, run a knife around edge of cake to loosen.
Dust lightly with confectioner’s sugar. Place a clean kitchen towel on top and quickly flip the cake on to a clean work surface. Lift and remove the pan. Remove and discard the parchment paper, if necessary. Dust lightly with confectioner’s sugar. Starting with the long side, carefully roll up the cake in the kitchen towel. Transfer to a sheet pan or plate and place seam side down. Refrigerate until cool, at least one hour.
Once the cake has cooled, return it to a clean work surface. Gently unroll the cake. Spread raspberry jam across the cake to within about ½-inch of the edge. Snugly reroll the cake in the cloth and return to the refrigerator to chill until firm, about one hour. (Cake can be made a day ahead, but will need the added precaution being sealed in plastic wrap.)
When ready to slice, remove from the cloth or plastic wrap and transfer to a clean work surface. Trim the ends then cut into pieces about ¼-inch thick. Tightly line the bowl with the slices of cake. Pour in prepared filling. Top with additional slices of cake. Chill until firm.