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 often, 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, the burner, and batch size. You'll know it's done when the vinegar has thickened to the point where the simmering bubbles linger on the surface 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 reduce it further. If the glaze is too thick, you can thin it with a small splash of water.
Once cool, drizzle the glaze over your favorite foods and enjoy! Refrigerate leftovers until ready to use, or up to three weeks.