Preheat the Oven: Heat oven to 425°F (220°C) and coat a 9x13-inch baking pan with cooking spray.
Mix the Vegetables: In a large bowl, combine potatoes, carrots, onion, balsamic vinegar, butter, thyme, garlic, salt, and pepper.
Arrange in Pan: Spread the vegetable mixture evenly into the prepared baking pan and cover with foil.
Roast Covered: Roast for 45 minutes, shaking the pan every 15 minutes for even cooking.
Roast Uncovered: Remove the foil and continue roasting uncovered for 30 more minutes, stirring occasionally, until caramelized and tender.