Preheat the oven to 400 degrees. Add the balsamic vinegar to a small bowl and the brown sugar to another. Set aside.
Trim the Brussels sprouts, cutting the medium and large ones in half lengthwise. Leave the small ones whole. Dip the Brussels sprouts in the vinegar and then roll in the brown sugar. Then wrap each Brussels sprout with a piece of bacon. Arrange on a rack set over a sheet pan.
Bake for 15-20 minutes or until bacon is browned and crisp. Brush the sprouts with extra balsamic vinegar. Garnish with shaved parmesan. Serve.