To make the cake, position a rack in the top third of the oven and preheat to 375° F.
Lightly butter a 10 X 15-inch jelly roll pan.
To line the bottom and sides of the pan, cut a 12 X 16-inch piece of parchment or waxed paper.
At each of the four corners, cut a diagonal slash about 2 inches long.
Fit the paper into the pan, folding the cut ends over each other at the slashed to form neat corners.
Lightly butter and flour the paper, tapping out the excess flour.
In a large bowl, using a hand-held electric mixer set at high speed, beat the sugar and eggs until light in color and texture, about 3 minutes.
(The mixture should form a thick ribbon that falls back on itself when the beaters are lifted about 2 inches from the bowl. It must be stiff enough to support the weight of the dry ingredients.) Stir in the pumpkin and lemon juice.
Sift the flour, cinnamon, ginger, baking soda, salt, nutmeg, and cloves onto a piece of waxed paper.
With the mixer on low, gradually beat in the flour mixture, scraping the sides of the bowl as needed.
Spread the batter evenly into the prepared pan, being sure to reach into the corners.
Sprinkle the batter with the walnuts.
Bake until the center of the cake springs back when lightly pressed with a finger, about 15 minutes.
Sift confectioners' over the top of the cake.
Place a clean kitchen towel over the cake, then top with a baking sheet.
Holding the baking sheet over the cake, turn the cake upside down and invert it onto the towel on the baking sheet.
Carefully peel off the paper.
Place the paper back on the cake.
Using the towel as an aide, roll up the cake and cool completely.
To make the filling, in a medium bowl, using a hand-held electric mixer at medium speed, beat the cream cheese, butter, and vanilla until combined.
Gradually beat in the confectioners' sugar until smooth.
Unroll the cake and discard the paper.
Spread the filling evenly over the cake and sprinkle with the crystallized ginger.
Re-roll the cake (you won't need to use the kitchen towel) and wrap in plastic wrap.
Refrigerate until the filing is firm, at least 1 hour.
(The cake can be refrigerated for up to 2 days.) To make the spiked cream, in a chilled medium bowl, using a hand-held electric mixer set at high speed, beat the cream, confectioners' sugar, optional rum, and vanilla until stiff.
Transfer to a pastry bag fitted with a large open star tip.
Transfer the roll to a long serving platter.
Garnish the cake with swirls of the whipped cream, and sprinkle with the walnuts and crystallized ginger.
To serve, cut the cake diagonally into thick slices.