Add the white rum, lime juice, simple syrup, chile liqueur, and mint leaves to a cocktail shaker.
Gently muddle the mint to release its oils without tearing the leaves.
Add ice and shake vigorously for 10–15 seconds, until thoroughly chilled.
Double strain evenly between two glasses filled with fresh ice.
Top each glass with 4 oz soda water and gently stir to combine.
Garnish with a sprig of fresh mint and a jalapeño slice.