3 russet potatoes (2 pounds total), scrubbed, quartered lengthwise, and cut crosswise into 1 1/2-inch pieces
1 large celery root (1 1/2 pounds), peeled and cut into 1-inch pieces
1 bunch carrots (7 medium), peeled and cut on the bias into 3-inch pieces
3 large leeks (2 pounds total), white and pale-green parts cut crosswise into 1 1/2-inch rounds, washed well, and drained
1/4 cup extra-virgin olive oil
Coarse salt and freshly ground pepper
2 tablespoons white-wine vinegar
1/3 cup lightly packed fresh mint leaves and small sprigs, for serving
Preheat stove to 375 degrees with racks in upper and lower thirds. On a rimmed baking sheet, throw vegetables with oil. Season with salt and pepper. Move half of vegetables to one more rimmed baking sheet. Spread vegetables in a solitary layer.
Cook, turning baking sheets start to finish and front to back partially through, until vegetables are delicate and brilliant brown in spots, 50 to an hour. Move to a platter and throw with vinegar. Sprinkle with mint and serve.