In a medium saucepan, bring balsamic vinegar and brown sugar to a boil over medium heat, stirring constantly until the sugar dissolves. Once bubbling, reduce heat slightly and allow to cook until thickened, 10-20 minutes. Allow the cooked vinegar to cool slightly. It will continue to thicken as it cools.
Meanwhile, prepare couscous according to package directions. Once fully cooked, add basil, tomatoes, mozzarella, and olive oil to taste, stirring gently to incorporate everything. Divide amongst bowls and drizzle with the balsamic vinegar reduction. Alternatively, transfer the entire couscous mixture to a large bowl and drizzle balsamic reduction over the top. Serve warm or at room temperature.