Preheat oven to 400°F. In large skillet over medium heat, bring balsamic vinegar and brown sugar to boil, stirring until sugar dissolves. Reduce heat and simmer until vinegar thickens slightly, about 3 minutes. Add butter and salt and stir until butter melts. Add potato pieces to skillet; toss to coat. Season potatoes with freshly ground black pepper. Spread potatoes evenly on rimmed baking sheet. Bake until potatoes are tender and golden, stirring occasionally, about 40 minutes.

Transfer potatoes to large platter or bowl and serve.