Add the cranberries, water, erythritol, and salt to a small-medium saucepan over medium heat.
As soon as the liquid starts simmering, cover the pan and cook until the cranberries are burst and it has a jam-like consistency, about 8 minutes. (Watch it closely and turn the heat down if needed so it doesn’t boil over.) Use a fork to mash up the cranberries a bit.
Turn off the heat and stir in the vanilla and rosemary.