Place vinegar and garlic in small non-reactive saucepan over medium heat. Bring to a boil. Reduce heat to low; gently boil for 25 to 35 minutes, or until vinegar has become thick enough to coat the back of a spoon. (Watch vinegar carefully after 20 minutes of cooking to avoid burning.)
Remove from heat; cool. Remove garlic. Set aside.
Heat a medium cast iron (or nonstick) skillet over medium-high heat for 4 to 5 minutes.
Place Brussels sprouts in skillet, cut side down, in a single layer; cook for 4 minutes, or until browned.
Add salt; cook for 1 to 2 minutes.
Add water; cook until water has evaporated.
Top each serving with 1 Tbsp. balsamic glaze; serve immediately.