Preheat the oven to 400°F.
Dust the work surface with sugar and roll out the dough to 6 x 9 inches. Dust the surface of the pastry with sugar. Cut into six 3-inch squares. Moisten the baking sheet with water, place the pastry squares on the sheet, and allow to rest for 30 minutes. Bake for 10 - 15 minutes, until the surface has caramelized. Remove from the baking sheet while still hot and cut each slice in half horizontally.
To make the filling. bring the cream to a boil, remove from the heat, and add the chopped couverture, stirring constantly until melted. Place a hand blender in the cream, switch on, and blend thoroughly, using a circular motion and not allowing the blender to come to the surface. Allow to cool. Whip with a hand mixer until frothy and add the rum. Using a pastry bag with a star tip, pipe a double ring onto the bottom half of each pastry square.
To make the sauce, break open the pomegranates and mix the seeds in a saucepan with the other ingredients. Simmer over a low heat until the mixture has reduced by half. Cool and strain.
To decorate, whip the cream with the sugar to soft peaks and stir in 3 - 4 tablespoons of the sauce. Place a spoonful of whipped cream on the cream filling, top with the other half of the pastry square, and add the sauce and pomegranate seeds.