In a standard steamer (basket and base), combine the 3 cups water, the salt, and the rosemary sprigs. Bring to a boil over medium-high heat.
Place the washed potatoes in the steamer basket. Place the basket in the steamer base. Cover the steamer, reduce the heat to medium, and cook for about 30 minutes, until the potatoes are tender but not cracked.
Carefully remove the potatoes from the steamer and let stand 5 minutes.
Combine butter and chopped rosemary in a small microwave-safe bowl; microwave at HIgH 20 seconds or until butter melts.
Drizzle butter over potatoes. Serve.