With the rack in the middle position, preheat the oven to 180°C (350°F).
In a saucepan over medium heat, soften the onion in the butter. Add the barley and cook for about 2 minutes, stirring constantly. Season with salt and pepper. Add the broth and bring to a boil. Reduce the heat, cover and simmer gently until the barley is tender, 30 to 40 minutes.
Meanwhile, in an ovenproof non-stick skillet over medium-high heat, brown the rutabaga, carrots and thyme in the oil. Season with salt and pepper. Transfer to the oven and roast, stirring frequently, until the vegetables are tender, about 30 minutes.