Preheat the oven to 325 degrees. Line a 12-by-17-inch rimmed baking sheet with parchment paper. In a large bowl, using an electric mixer, beat the egg yolks until pale, about 2 minutes. Add the molasses, 1/4 cup brown sugar and the fresh ginger and beat until combined. In a medium bowl, whisk the flour, baking powder, ground ginger, allspice, black pepper and salt. Beat the dry ingredients into the egg yolk mixture until combined.
In a clean bowl, using clean beaters, beat the egg whites until soft peaks form. Gradually add 1/4 cup of the granulated sugar and beat until firm and glossy. Fold the egg whites into the batter until no streaks remain. Spread the batter onto the prepared baking sheet in an even layer. Bake for about 15 minutes, until lightly browned and firm to the touch. Transfer to a rack and let cool for 10 minutes.
Sprinkle the cake with the remaining 2 tablespoons of granulated sugar. Run the blade of a sharp knife around the edge of the pan. Cover the cake with a clean kitchen towel and top with a large cutting board. Holding the pan, towel and cutting board, invert the cake onto the cutting board. Remove the pan and carefully peel off the parchment paper. Cover loosely with a kitchen towel and let the gingerbread cool completely.
Make the Filling: In a small microwave-safe bowl, sprinkle the gelatin over the cold water; let stand until softened, about 5 minutes. Microwave at high power until the gelatin is melted, about 10 seconds. In a clean bowl, beat the cream cheese with the cinnamon and melted gelatin until smooth. In another bowl, whip the creme fraiche with the confectioners' sugar until stiff. Fold the cream cheese into the creme fraiche.
Spread the filling evenly over the entire surface of the cake. Starting at a short end roll up the cake jelly roll-style. Wrap the gingerbread roll tightly in pastic and refrigerate until firm, at least 3 hours.
Sauce: In a small saucepan, melt the butter. Add 1/3 cup brown sugar and bring to a boil, whisking constantly. Add the cinnamon sticks and cloves, Whisk in the rum and cider and remove from the heat. Let the butter-rum sauce steep for 1 hour. Discard cinnamon sticks and cloves.
Upwrap the gingerbread roll and transfer it to a plate; dust lightly with confectioners' sugar. Cut into slices and bring to room temperature. Garnish with pecans and cranberries and serve with the butter-rum sauce.
Make ahead: The finished roll can be refrigerated overnight. The sauce can be refrigerated for up to 3 days; reheat gently before serving.