Cook the cranberries with the water, cinnamon stick, bay leaf, cardamom, and salt in a large skillet or pot, stirring occasionally, until they’re just beginning to split.
Add the oranges, smashing them with the back of a spoon to release the juices. Continue to cook until the cranberries are as soft as you’d like.
Remove from the heat and stir in the lingonberry jam. Give it a taste and add a little sugar if needed.
Chill until cool, then stir in the pomegranate seeds.