Place carrots in a saucepan and cover with water; bring to a boil. Reduce heat to medium-low and simmer until tender, 10 to 12 minutes. Drain and transfer carrots to a serving dish.
Heat butter in the same saucepan over medium heat; add brown sugar, mustard, ginger, and salt. Cook and stir until sugar is dissolved, 2 to 3 minutes. Pour sauce over carrots; toss to coat.
