Adjust oven rack to the lower third position; preheat oven to 400°F. For easy clean up, line a large baking sheet with aluminum foil.
Wrap the prepared dough in plastic wrap; chill in the refrigerator.
Put the prepared vegetables on the baking sheet, drizzle them with the olive oil and a generous sprinkling of the salt and pepper. Toss to coat. Then arrange in what approximates a single layer. Bake in the preheated until the veggies are fork tender and slightly caramelized -- about 30 minutes. Transfer to a wire rack to cool.
While the veggies are cooling, tip the sugar and water into a large non-stick oven-proof skillet. Set the skillet over medium heat, and let cook, while swirling the skillet occasionally, until the sugar melts and turns amber-colored. Immediately remove from heat, and swirl in a pinch of salt and the vinegar. Scatter the rosemary and sage leaves over the caramel.
On top of the caramel, arrange vegetables (omit onions for now) in some decorative fashion in a single layer. Use small ends of carrot and parsnip to fill in the gaps. Then toss, in no particular fashion, the remaining sweet and white potatoes, turnips, and etc. over the first vegetable layer. Finally, strew the onions over the top.
On a lightly floured surface, roll the pastry out to a 12-inch-diameter disk. Poke 5-6 steam vents in the center of the disk. Then drape the disk over the vegetables, tucking the edges down into the caramel (don't be too fussy with the "tucking" job). Bake in the 400°F oven (again, on the lower-third rack) for 20 minutes. Then reduce the temperature to 350°F, and continue baking until the crust colors -- about 20 minutes.
Remembering to use an oven mitt to protect your hand from the red-hot handle, transfer the skillet to a wire rack. Cool for just 5 minutes.
Set a large plate or round platter over the skillet. Invert to unmold the tart. Use a pastry cutter to divide the tart into 8 wedges. Serve hot or warm. Leftover -- if they are any -- are delicious cold from the fridge!