Make the cake: Preheat the oven to 375 degrees F. Line a rimmed baking sheet with parchment paper. Spray the parchment paper with cooking spray. Sift the flour, cinnamon, ginger and allspice into a small bowl. In a large bowl, beat the egg yolks, granulated sugar and brown sugar with a mixer until very thick. Add the pumpkin and beat on low speed until incorporated. Add the dry ingredients and beat until incorporated. In a separate bowl, beat the egg whites and salt with a mixer until stiff but not dry. Fold the egg whites into the cake batter with a rubber spatula until most of the white streaks are gone.

Spread the batter on the sheet pan and smooth the top. Bake until a tester comes out clean, 15 to 18 minutes. While the cake is hot, dust generously with confectioners' sugar. Loosen the edges and turn the cake out onto a kitchen towel; peel off the parchment paper. Starting from one long side, roll up the cake around the towel. Turn seam-side down, put on the baking sheet and transfer to the refrigerator to cool completely, about 1 hour.

Make the filling: Combine the gelatin and rum in a saucepan over low heat and stir until the gelatin dissolves. Let cool. Beat the heavy cream and confectioners' sugar in a large bowl with a mixer until peaks form. Fold in the gelatin mixture and 6 tablespoons toffee pieces.

To assemble, unroll the cake and sprinkle with the remaining 4 tablespoons toffee pieces. Spread the cream filling over the toffee. Roll the cake back up to encase the filling. Place the cake seam-side down on a platter and trim the ends. Dust with confectioners' sugar. Use a serrated knife to cut the cake crosswise into 1-inch-thick slices. Spoon some warm caramel sauce and toffee pieces on top.

Photograph by Con Poulos