Put the lime juice in a large jug and top up with water until you have 200ml liquid. Add the zest and mint, then stir in the sugar, cinnamon and vanilla paste. Cover and leave to infuse in the fridge for at least 1 hr or overnight. Stir well to make sure the sugar has dissolved, then strain into a clean 1.5-litre jug and stir in the vinegar and rum. Chill until ready to use, or for up to 12 hrs.

To make the cocktail, stir in the mint leaves, lime pieces and a generous handful of ice.

Top up with 600ml sparkling water and pour into tall glasses with more ice, adding a little more sparkling water, if you like. Garnish with mint sprigs to serve.