Add the blueberries to a small saucepan over medium heat. Add the brown sugar and balsamic vinegar. Cook over medium heat for 10 minutes, stirring occasionally.
Meanwhile, in a small bowl, beat the goat cheese and cream cheese together.
Spread the goat cheese mixture over a small plate and top with the blueberry mixture that has been allowed to cool for a few minutes.
Serve the dip with some crusty French bread or crackers.