Heat the oven to 350 degrees. Using about 1 1/2 teaspoons of butter, generously butter a 9-by-13-inch baking dish.
Trim the root ends and 1 1/2 inches off the green tops of the scallions. Arrange half of the scallions in the baking dish so the bulb ends are lined up at one end and the greens are toward the middle. Place the other half of the scallions in the opposite direction, so you end up with a double layer of scallion greens across the center of the dish and a single layer of bulbs and each end of the dish.
Pour the water into the dish. Cut the remaining butter into slivers and dot it over the top of the scallions. Season with the tarragon or parsley, salt, and pepper. Cover the dish tightly with foil, and slide onto the middle rack in the oven. Braise undisturbed until fragrant and tender, 35 to 40 minutes.
Remove the foil from the dish, and increase the oven heat to 450 degrees. Roast the scallions for 10 minutes, then shake the pan back and forth to coat the scallions with the glaze that will have formed. Continue roasting until the liquid evaporates and the edges of the scallions are beginning to brown, another 5 minutes or so. Squeeze over a few drops of lemon juice to taste, and serve hot or warm.