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First, make the syrup. Heat the sugar and 100ml water in a pan over a medium heat until the sugar has dissolved. Turn off the heat and stir in the peppermint extract. Leave to cool completely. You will make more syrup than you need – any leftovers will keep chilled for up to three days.
Pour the lime juice into a tall glass. Add the rum, 15ml of the mint syrup and a handful of ice. Stir well, then top up with the sparking water. Stir gently to combine, then garnish with the candy cane.