Place the balsamic vinegar in a medium-sized saucepan set over medium-high heat. The wider the saucepan, the faster the balsamic will reduce (see notes for more info).
Once the balsamic is simmering, reduce the heat to medium or medium-low and continue simmering, stirring occasionally, until the desired consistency is reached (for me that means reducing until only around 1/4 of the liquid remains. It's slightly thicker than maple syrup).
Remove from the heat and cool for several minutes. Transfer to an airtight container and store in a cool, dry place. I typically use it within 3 months, but it can probably keep for longer.
Notes
Recipe yields approximately 3/4 cup total, but you can reduce it by more or less depending on how thick you want it. Keep in mind that the reduction might thicken slightly as it cools. If you accidentally over-reduce the vinegar, whisk in some warm water until it thins out.You can scale the recipe up or down to make however much you need, but this will alter the total time.Equipment: I used this saucepan in the photos, but I recommend using a wider pot like a sautoir or enameled cast iron Dutch oven to speed up the process. More surface space against the stovetop can dramatically cut the total reduction time, and simmering vinegar is smelly. You might want to open a window or turn on the kitchen vent!