Preheat your oven to 425°F and line two large baking sheets with parchment paper.
In a large bowl, combine all the chopped vegetables with olive oil, thyme, salt, and pepper. Toss everything together until the veggies are evenly coated.
Spread the vegetables in a single layer on the prepared baking sheets, making sure not to overcrowd them (this helps them roast instead of steam).
Roast for 35-40 minutes, stirring once halfway through, until the vegetables are golden brown and fork-tender.
If using balsamic vinegar, drizzle it over the roasted vegetables and toss gently before transferring to a serving platter. Serve warm and watch them disappear!