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Cut the carrots into ribbons with a vegetable peeler and set aside. Pour 500ml water into a large saucepan with the salt and bring to the boil. Add the carrot ribbons and teabags and remove from the heat. Leave to steep for 20 mins until the mixture is cold and the ribbons have softened. Pour into a smaller container and chill until needed. Once cold and ready to serve, strain the carrot ribbons, discard the brine and pat dry with kitchen paper or a clean tea towel.
Spread the baguette slices with the cream cheese. Top each toast with a few carrot ribbons and a pinch of the dried seaweed, then season and serve.