Put the beetroot and carrots in a roasting tin. Drizzle over the olive oil, sprinkle with the cumin seeds and season well with salt and pepper, then toss until the roots are evenly coated in the oil. Roast in a preheated oven, 200°C (400°F), Gas Mark 6, for 30–35 minutes until tender.
Meanwhile, cook the quinoa in a saucepan of boiling water for 10–12 minutes until tender, then drain. Tip into a large bowl, add the chickpeas, onion, mint and hazelnuts and toss together.
Mix the lime juice, tamari or soy sauce and sesame oil together in a jug, pour over the quinoa mixture and gently toss together. Add the roasted beetroots and carrots and lightly mix through.