Place brown sugar in a small saucepan with about 2 tablespoons of water. Apply heat just to melt the sugar and water to a thickened consistency. Add the vinegar and stir. If needed, reduce very gently over a low flame until desired thickness is achieved. (The balsamic will thicken once cold as well.) The longer heat is applied, the less the flavor resembles an aged balsamic vinegar, so try not to scorch or overheat.
Recipe by Chef/Co-owner Brian Kingsford, Bacaro, Providence