Fry onion in a little olive oil until soft and translucent but not browned.
Add balsamic. It will give off a pungent hint of vinegar, then add brown sugar and stir in well. By now that vinegar hint should be gone. Continue to cook at medium temperature until you reach desired colour, about 5 minutes.
This is a highly adjustable recipe. You can always add in a splash more vinegar and a pinch more sugar if you wish, or add less the next time round, depending how you like it. The trick is the portion of vinegar to sugar should be about equal.
Use the onions as a condiment, on pizza bases with some goats cheese, as a topping on savoury tarts.