In a medium saucepan, combine the sugar with 1 cup / 237 ml of the water.
Bring to a simmer over medium heat, stirring until the sugar is completely dissolved to create a simple syrup.
Add the cranberries to the saucepan.
Bring back to a simmer, then cover and cook for 10 minutes. You'll hear the cranberries begin to pop.
Uncover the saucepan, reduce the heat slightly, and continue to simmer for another 10 minutes, stirring occasionally, until the sauce has thickened.
While the cranberries cook, cut the unpeeled orange into rough chunks.
Place them in a food processor and pulse until finely chopped but not puréed.
Stir the chopped orange, the remaining ½ cup / 118 ml (4 fl oz) of water, ground ginger, cinnamon, cloves, and crushed cardamom seeds into the cranberry mixture.
Continue to simmer for 20 more minutes, stirring frequently to prevent sticking, until the relish is thick and fragrant.
Remove from heat and let it cool completely.
Transfer to a jar or bowl, cover, and chill in the refrigerator for at least 2 hours before serving. The relish will continue to thicken as it cools.
Don't skip the chilling step. The relish thickens considerably as it cools, developing its final, perfect consistency in the refrigerator.