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Blanch carrots in a pan of boiling salted water for 3 mins, drain well, then pat dry. In a large pan, melt the butter and oil, then fry the carrots, onions and thyme over a low heat for 30 mins until golden.
Stir in the sugar and red wine and bubble for a few mins to boil off the alcohol. Add the vinegar, then continue to cook until syrupy, about 5 mins. Remove the sprigs of thyme and serve. Make up to 2 days ahead, stored in a covered container. Tip back into a pan and reheat or use a microwave.