Peel the onions and thinly slice (this can be done in a food processor).
Take a medium or large sized saucepan or pot and heat the olive oil. Cook down the onions over a medium to high heat stirring often for around 10 minutes until soft and translucent.
Add the brown sugar and stir over heat until the sugar dissolves then add the balsamic vinegar and stir.
Reduce to a low heat stirring occasionally for around 40 minutes until the balsamic has reduced to the stage that the onions are nicely coated.