Cut the lime into 6 wedges. Place the lime wedges and 10 fresh mint leaves in a highball glass.
Add 2 teaspoons granulated sugar. Use a muddler or the back of a wooden spoon to gently muddle the mint and lime until the mint releases its oils and the sugar starts to dissolve.
Pour in 1.7 fl oz of white rum. Stir gently to help dissolve the sugar.
Fill the glass with crushed ice.
Top off with soda water and stir gently from bottom to top to combine without losing the fizz.
Garnish with a sprig of mint and a lime wedge. Serve immediately.