In a small bowl, sprinkle the gelatin on the water and let bloom for 5 minutes. Set aside.
In a saucepan off the heat, combine the brown sugar and flour. Add the eggs and whisk until smooth.
Gradually whisk in the milk and cream. Bring to a boil over medium heat, whisking constantly and scraping the sides and bottom of the pan. Simmer over low heat,
1 to 2 minutes. Remove from heat and add the gelatin, stirring until dissolved. Add the butter, stirring until melted. Stir in the rum and vanilla. To prevent a skin from forming, lay a sheet of plastic wrap directly on the surface of the hot cream. Let cool.
Refrigerate until chilled, about 2 hours.
With the rack in the middle position, preheat the oven to 190°C (375°F). Line a 30 x 43-cm (12 x 17-inch) baking sheet with parchment paper, letting the paper hang over 2 opposite sides. Butter the unlined sides and the paper.
In a bowl, combine the flour, cocoa powder, spices and salt. Set aside.
In another bowl, cream the eggs and brown sugar using an electric mixer. Beat until the mixture turns pale, triples in volume and falls in ribbons from the beaters, about 10 minutes. Using a spatula, gently incorporate the melted chocolate.
Sift the flour mixture onto the egg mixture and, using a spatula or whisk, gently fold it into the egg mixture.
Spread the batter onto the baking sheet. Bake until a toothpick inserted in the centre comes out clean, about 10 minutes.
Remove the cake from the oven. While the cake is still warm, invert it onto another sheet of parchment paper. Remove the paper from the top of the cake. Starting
from the shortest side, roll the cake and paper into a log shape. Let cool completely.
WHITE CHOCOLATE WHIPPED CREAM
In a large bowl, combine the chocolate, 60 ml (1/4 cup) cream and the sugar using an electric mixer. Gradually beat in the remaining cream and whip until stiff peaks form.
Unroll the cake and discard the parchment paper. Spread the top of the cake with the pastry cream. Roll the cake into a log and place on a serving plate. Frost the cake with the whipped cream and refrigerate until ready to serve.