Special equipment: a 10 1/2-by-15 1/2-inch rimmed baking sheet a large clean kitchen towel (preferably not terrycloth or microfiber)
For the cake: Position an oven rack in the middle of the oven and preheat to 350 degrees F. Line a 10 1/2-by-15 1/2-inch baking sheet with parchment paper so it fits the bottom snuggly. Butter and flour the parchment and the sides of the baking sheet.
Whisk together the flour, baking powder, cinnamon, ginger, pepper, allspice and 1/2 teaspoon salt in a large bowl and set aside.
Beat the egg yolks and 3/4 cup granulated sugar with an electric mixer on medium-high speed in a large bowl until the mixture is thick and falls into heavy ribbons when the beaters are lifted, about 5 minutes. Beat in the melted butter, molasses and vanilla. Sift the spiced flour mixture into the egg yolk mixture and use a rubber spatula to gently fold together until just incorporated.
Rinse the egg beaters and beat the egg whites and remaining pinch salt with an electric mixer on medium-high speed in a large bowl until frothy. Add the remaining 1 tablespoon granulated sugar and continue to beat until soft peaks form.
Fold one-third of the whipped egg whites into the cake batter to loosen it up a bit. Then gently fold in the remaining whipped egg whites until just combined. Pour the cake batter into the prepared baking sheet and spread it out in an even layer. Bake until the middle of the cake springs back when pressed, 12 to 15 minutes.
To roll up or train the cake: While the cake is still hot, use a knife to cut around the sides of the baking sheet to release the cake. Dust the cake with confectioners' sugar. Spread a large clean kitchen towel (preferably not terrycloth or microfiber) over the top of the cake. Quickly invert the baking sheet onto the towel. Tap the bottom of the baking sheet and slowly lift up; the cake should release and be positioned squarely on the towel. Carefully peel away the parchment paper, making sure not to tear the cake. Trim away any rough edges if desired. Then, while the cake is still warm and starting at the long side of the cake, roll it up into a tight log, taking the towel with it. Let the cake cool completely, rolled up just like this, about 30 minutes.
For the filling: Beat the cream cheese and butter with an electric mixer on medium-high speed in a medium bowl until smooth. Add the confectioners' sugar, lemon juice, vanilla and salt and beat until thick and smooth. Set aside 2 tablespoons of the filling.
To fill and roll the cake: Unroll the cooled cake and spread the filling over the top in an even layer. Then roll the cake back up (without the towel this time) and put it seam-side down on a serving platter. Dip each gum drop in some of the reserved filling and evenly space them down the center of the roulade. Dust the cake with more confectioners' sugar. Slice and serve.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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