Add the carrots, water, brown sugar, butter, salt, and rosemary sprigs to a large skillet. Place over high heat and bring to a boil.
Reduce the heat to medium-low. Simmer for 30 minutes or until the carrots are tender.
To serve, transfer the carrots and any glaze in the pan to a serving bowl. Remove the rosemary sprigs and sprinkle with chopped fresh rosemary for garnish.