Remove any leaves or stalk from the beetroot (do not peel the roots), then scrub thoroughly. Cook the beetroot in a saucepan of boiling, salted water for 30 to 40 minutes, until it is soft when tested with a skewer. Drain and cool it under running water.
Heat the oil in a large saucepan and cook the onions for 8–10 minutes over a moderate heat, stirring, until they are softened and golden.
Pour the vinegar over the onions and scrape the bottom of the pan with a wooden spatula to remove any sediment. Add the curry powder, honey, thyme sprig, 1 1/2 tablespoons of water and a pinch of salt. Cover and cook gently for 20 minutes, stirring frequently.
Peel and slice the beetroot, then finely chop it in a food processor. Add to the onions and simmer for 5 minutes. Remove the cooked thyme before serving and garnish with a fresh sprig.