In a small saucepan, combine the balsamic vinegar, brown sugar and soy sauce. Bring the mixture to a boil. Lower the heat and simmer until the mixture is thick enough to cover the back of the spoon.
Combine the mayonnaise, mustard and garlic together in a small bowl.
Spread the mustard mixture on one side of your roll and the other side with Brie cheese. Top one half of the sandwich with chicken and drizzle with balsamic glaze. Add any toppings to the opposite side and put the sandwich together.