Mix half the oil with the garlic, cumin, cinnamon, turmeric and chilli flakes in a large bowl and add the chicken breasts. Leave to marinate for half an hour if possible.
Heat oven to Gas Mark 4, 180°C (350°F). Place the carrots, parsnips, potatoes, onions, garlic and thyme sprigs in a roasting tin. Add the remaining olive oil and stir the vegetables to cost in the oil. Add in the chicken breasts and season everything with salt and black pepper. Roast for 30 minutes.
Combine all the ingredients for the Spicy Mayonnaise and serve with the roasted chicken breasts and vegetables.