Bring the water, butter, salt and green beans to a boil in a Dutch oven or large deep skillet. Cover and steam over medium-high heat until the vegetable is brightly colored and just tender, 5 to 10 minutes.
Remove the lid and continue to cook until the liquid evaporates, 1 to 2 minutes longer, adding the tarragon at this point. Saute to intensify flavors, 1 to 2 minutes longer. Adjust seasonings, including pepper to taste, and serve.
Recipe courtesy of Pam Anderson's How to Cook Without a Book. Published by Broadway Books, 2000.