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Heat the butter in a large, heavy-based frying pan and add the onions. Cook over a medium heat for 6-8 mins, turning occasionally, until golden and caramelised. Meanwhile, cook the brussels sprouts in a pan of boiling salted water for 3-4 mins until just tender.
Stir the sugar and vinegar into the onions and allow to bubble for a few secs. Remove from the heat, drain the sprouts thoroughly and toss through the onion mixture to serve.