In a medium saucepan over medium heat, combine the chopped apples, cranberries, brown sugar, apple cider vinegar, water, grated ginger, cinnamon, ground cloves, and a pinch of salt.
Bring the mixture to a gentle boil, then reduce the heat to low and simmer, stirring occasionally, for about 20-25 minutes or until the fruits soften and the mixture thickens.
As it simmers, use a spoon to occasionally mash some of the fruit against the side of the pan to achieve your desired consistency.
Once thickened to your liking, remove the chutney from the heat and let it cool. It will continue to thicken as it cools down.
Transfer the Apple-Cranberry Chutney to a clean jar or airtight container. Refrigerate once completely cooled.