To make the syrup, place the sugar and water in a saucepan over low heat and stir until the sugar dissolves. Bring to a boil, then remove from the heat. Let the syrup cool to 122°F (50°C). Stir in the rum.
Place the baba on a wire rack with a dish underneath to catch drips. Ladle over the hot syrup until the baba is thoroughly soaked. Alternatively, place the b