Preheat the oven to 200°C.
Heat some of the olive oil in a large tagine set over a moderate heat. Sauté the onion for 4-5 minutes, stirring occasionally. Add the carrot, potato, cauliflower and courgette and a little more olive oil stirring well to combine.
Sprinkle over the spices, stir well again and cook for a further 3-4 minutes. Cover with a lid and transfer to the oven. Cook for 30-40 minutes until the vegetables are cooked and nicely coloured.
Remove from the oven, then season to taste and garnish with thyme sprigs before serving.