Place all cleaned and cut veggies in a large bowl, drizzle with oil, and sprinkle with cayenne pepper, dried thyme, and salt. Toss to coat veggies with oil and spices.
Place the coated veggies in a roasting pan or sheet pan that's been sprayed with cooking spray. Roast in oven, stirring every 15 minutes, until veggies are browned on the edges and tender when pierced with a fork, about 1 - 1.5 hours. If the veggies start to dry out too quickly, add some water to the pan.
Carefully remove the pan of roasted veggies from the oven, and sprinkle with white wine vinegar, if desired. Allow to cool slightly, and serve. Enjoy!