Heat a cast-iron skillet over charcoal briquettes or the glowing embers of a wood fire, or preheat a heavy ovenproof skillet or roasting pan in a 400-degree oven.

In a small bowl, mix together the butter, olive oil, and balsamic vinegar. In a large bowl, toss the carrots, parsnips, rutabaga, and onions with half of the butter-oil mixture. Season the vegetables with salt and pepper to taste. Place the seasoned root vegetables into the hot skillet. If cooking over a fire, cover with foil and roast approximately 15 minutes. If cooking in an oven, do not cover, and cook approximately 15 minutes.

Toss the eggplants, zucchini, yellow squash, and mushrooms in a large bowl with the rest of the butter-oil mixture. Season with salt and pepper to taste and add to the pan with the root vegetables. Roast, covered if over an open fire and uncovered if in the oven, until the onions are soft, about 15 more minutes.

Remove the pan from the fire or the oven and stir in the thyme and tomatoes. Serve immediately.