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Melt the butter in a shallow saucepan over a medium heat until nut brown, then add the carrots and star anise, and cook for 5 mins until the carrots start to colour. Sprinkle over the sugar and just cover with water. Season with salt, then bring to the boil, reduce the heat to a steady simmer and cook for 8 mins until most of the water has evaporated and the carrots are just cooked through and coated in a buttery glaze. Can be made up to four hours ahead and kept at room temperature, or cooled then kept chilled overnight.
About 5 mins before serving, bring the carrots back to a simmer, stir through the sprout petals and cook for 3-5 mins until just wilted.