1. Lop off the two ends of the orange. With a sharp, serrated knife, cut the orange into 1/3-inch (1cm) slices.
2. In a medium-sized nonreactive saucepan, cover the orange slices with cold water. Bring to a boil, reduce heat, and cook at a low boil for 10 minutes. Drain. Return the oranges to the saucepan. Cover with water again, bring to a boil, and cook for another 10 minutes. Drain and rinse with cold water.
3. Return the orange slices to the saucepan, add 3/4 cup of water and granulated sugar. Bring to a boil then reduce the heat to a low boil and cook until the liquid is reduced to a thick syrup. During cooking, turn the oranges a few times in the reducing syrup so that they candy evenly.
4. As the liquid cooks down, close to when there is very little in the saucepan, monitor them closely turning them frequently to avoid burning them. Remove from heat once most of the liquid is evaporated. Tilt the oranges into a colander and let cool.
5. In the same saucepan, add the other 3/4 cup water, brown sugar, rum, cinnamon stick, vinegar, and allspice. Bring to a boil, add the cranberries, then reduce the heat slightly and cook until the cranberries pop and just start to fall apart. Chop the candied oranges into little pieces about the size of peas and add the candied oranges to the cranberries. Cook for about a minute, then remove from heat.