Scrub the turnips, there is no need to peel them, but they look a bit fancier if you do. Cut into 1 inch chunks.
Heat the oil in a large skillet and add the turnips (as you can see I did this in reverse, either way works). Cook for about 2 minutes or until the edges begin to brown. Stir a couple of times to make sure all sides get seared.
Add the juice, maple syrup and vinegar. Cover and bring to a boil (it will be almost instant). Reduce heat and simmer until the turnips are just tender.
While the turnips simmer and make the kitchen smell irresistible, make your mizuna nests. It looks nice, but cutting up the mizuna is probably better if you are planning to eat with others!
When the turnips are just tender, uncover and turn up the heat until the turnips are fully tender and the liquid is reduced to a syrup.
Remove from heat, stir in butter if using, and serve.
Karl added soy sauce and sesame seeds to his, but then tucked in before I could get a picture.