In a small bowl, stir together the miso and 2 tablespoons of the butter. Set aside.

Remove and discard (or reserve for another use) turnip stems, then coarsely chop the leaves. Slice the turnips in half, or leave them whole if tiny, and place in a large, heavy skillet. Add the water, mirin, last tablespoon of butter, and 1/8 teaspoon of salt. Bring to a boil over medium high heat and cover. Simmer, covered, for 10 minutes.

Stir in the greens, a handful at a time, and cook, covered, for 1 minute. Uncover and continue boiling, stirring occasionally, until tender and liquid has reduced, about 5 minutes. Stir in the miso butter, gently tossing the turnips to coat well, and cook for an additional minute before serving.