This is an easy onion jam that is incredibly versatile. It enhances anything from rice or barley dishes to spreading on a piece of bread. Great accompaniment to chicken as well. You can substitute sherry vinegar for the balsamic vinegar.
Heat olive oil in a saucepan over medium-high heat. Saute onion in hot oil until soft and caramelized, 10 to 12 minutes. Add water, balsamic vinegar, and brown sugar; stir until sugar is dissolved and mixture is simmering. Reduce heat to low and cook until mixture thickens and reaches desired consistency, about 30 minutes.