Add the balsamic vinegar and brown sugar to a small saucepot. Stir to dissolve the sugar.
Bring the mixture up to a simmer over medium heat. Reduce the heat to medium-low, then continue to simmer the mixture, stirring occasionally, until it has reduced in volume by about half. This should take around ten minutes, but the total time can vary depending on your cookware and burner. You'll know it's done when the simmering bubbles linger on the surface of the vinegar instead of immediately popping.
Remove the glaze from the heat and allow it to cool. It will thicken considerably more as it cools. If it isn't to your desired thickness, you can simmer the glaze again to further reduce.
Once cool, drizzle the glaze over your favorite foods and enjoy! Refrigerate leftovers until ready to use.