Preheat the oven to 350 degrees F.
Line a 12 by 8-inch brownie or cake pan 1 1/2 to 2-inches deep with parchment paper.
Melt the chocolate and butter together in a pan over simmering water, also known as a double boiler. Do not let the bottom of the pan touch the simmering water as the chocolate may scorch. Set aside the melted chocolate to cool slightly.
In a separate bowl, beat together the eggs and sugar, using either a whisk or an electric hand mixer, for around 5 minutes, or until the ingredients are nice and thick. Whisk in the chocolate and butter mixture, and then the rum, if using. Fold in the flour, and then the pecans, and preserved ginger. Stir just to incorporate the ingredients.
Pour the batter into the lined brownie pan. Bake the brownies for 20 to 25 minutes. They should be mostly cooked while still leaving a slightly gooey trace on a knife that you insert into the center of the brownie pan. Leave the brownies out to cool slightly, and then cut them into triangles or small squares. Decorate the brownies by dusting a little confectioners' sugar on top, if using.