Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper or foil. Scrub and trim the turnips, then dice into cubes. Transfer the turnips to the baking sheet, and toss with olive oil. Spread them out in a single layer, and roast for 20 to 25 minutes until tender and lightly browned. You may want to flip them halfway through cooking.
A few minutes before the turnips are finished roasting, combine the butter and miso in a small saucepan over medium-low heat. Cook, stirring frequently, until the butter and miso melt down. Stir in the syrup, vinegar, and soy sauce until smooth. Keep warm, and toss the turnips in the sauce before serving. Enjoy!
If you can't find Japanese turnips, you can substitute other varieties.
This dish is best eaten right away, but leftovers will last for a couple days in the fridge. Reheat for about one minute in the microwave.