In a medium saucepan, heat oil over medium heat. Add onion and cook until very soft, about 15 minutes, reducing heat if starting to crisp.
Stir in cranberries, ginger, brown sugar, vinegar and cloves, plus 2 tablespoons of water. Cook, uncovered, until cranberries pop. Let cool 10 minutes.
Place the Brie in a small baking dish. Spoon 2/3 cup cranberry chutney over top and bake 15 minutes. Serve immediately.