Prepare the vegetables: Heat oven to 425 degrees. Add the vegetables to a rimmed sheet pan. Add 2 tablespoons oil, the salt, pepper and thyme (if using), and gently toss vegetables to coat. Use your hands to spread the vegetables out into one layer, spacing them evenly all over the pan.
Transfer to the oven and roast until they are tender and browned, 30 to 40 minutes, stirring at least once during roasting for even cooking.
While vegetables roast, you can make yogurt sauce if you like: In a small bowl, combine yogurt, garlic, oil, salt and pepper. Taste and adjust seasoning. Cover and place in the refrigerator until ready to use.
Serve roasted vegetables with a dollop of garlic yogurt, if desired, and a drizzle of oil on top.
Tip:
If you’d like to swap these vegetables for denser vegetables, use any combination of carrots, potatoes, sweet potatoes, turnips, butternut squash and cauliflower, cut into 1-inch chunks. Add an extra tablespoon of oil and extra ½ teaspoon of salt. Roast for 40 to 50 minutes. These vegetables take longer to cook and absorb more oil while roasting.