In a large saucepan of salted boiling water, blanch the turnips until barely tender, about 1 minute.
Using a slotted spoon, transfer the turnips to a baking sheet to cool slightly.
Add the parsnips and carrots to the saucepan and bring to a boil, then simmer until barely tender, about 2 minutes; transfer the carrots and parsnips to the baking sheet.
Add the beets to the saucepan and simmer until just tender, about 5 minutes; transfer to the baking sheet and let cool slightly.
In a large bowl, toss the vegetables with the olive oil, thyme, sage and rosemary and season with salt and pepper.
Spread the vegetables in an even layer on 2 large rimmed baking sheets.
Roast for 20 to 25 minutes, until browned in spots.
Transfer the vegetables to a platter.
Drizzle with the vinegar and tamari, season with salt and pepper and toss to coat.