Preheat the oven to 425 degrees F (220 degrees C). Coat a 9x13-inch baking pan with cooking spray.

Mix potatoes, carrots, onion, balsamic vinegar, butter, thyme, garlic, salt, and pepper together in a large glass bowl. Spread mixture into the prepared pan in an even layer. Cover with foil.

Roast in the preheated oven, giving the pan a shake every 15 minutes to ensure even cooking, for 45 minutes.

Remove foil and continue to roast, uncovered, stirring occasionally, for another 30 minutes.