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Cook the beetroots in a pan of boiling water for 5-6 mins until just tender but still with a bite; add the carrots for the final 2 mins. Whisk together the vinegar, mustard, olive oil, chopped mint and sugar, and season.
Put the rice and lentils in a bowl. Add the carrots and beetroots, then pour over the dressing and toss to combine. Transfer to a serving platter and sprinkle over the hazelnuts, feta and mint leaves to serve.