Place the carrots and parsnips in a roasting tin, spray lightly with olive oil and season with salt and pepper. Roast in a preheated oven, 200°C (400°F), Gas Mark 6, for 1 hour or until the vegetables are very soft.
Meanwhile, 20 minutes before the vegetables have finished roasting, put the leeks in a large saucepan with the stock and 1 teaspoon of the thyme. Cover the pan and simmer for 20 minutes.
Transfer the roasted root vegetables to a blender or food processor and blend, adding a little of the stock if necessary. Transfer to the stock saucepan and season to taste. Add the remaining thyme, stir and simmer for 5 minutes to reheat.
Ladle into individual bowls and serve garnished with the thyme sprigs.