Prepare the Glaze:

1. In a medium saucepan, heat balsamic vinegar and brown sugar over medium-low heat until sugar is dissolved. Simmer, stirring frequently, until liquid has reduced by half (about 20 minutes). Glaze should be thickened slightly and have a syrup-like consistency.(It will thicken a bit more as it cools.) Let glaze cool, then store in a sealed container in the refrigerator until ready to use.

Cook the Carrots:

1. In a medium saucepan, add the carrots, 1 tablespoon of butter, sugar, and salt. Add enough water to cover the carrots. Bring to a boil then lower heat to a simmer. Cook until carrots are tender and water has nearly evaporated, about 8-10 minutes.
2. To serve: Warm 1/2 cup of the Balsamic Glaze in a small saucepan and add remaining 1 tablespoon of butter, stirring until melted and combined. Drizzle glaze over cooked carrots. Serve immediately with additional glaze on the side.