Muddle mint by adding a spoonful of sugar, a squeeze of fresh lime, and a few fresh mint leaves to a thick-rimmed glass using either a muddler or the end of a rolling pin, then crush until the scent of mint is released
Fill the glass with ice
Pour ½ cup lemon lime soda and ½ cup soda water to the glass, followed by ½ ounce of simple syrup and 1 pull of tincture (preferably glycerin-based)
Stir to taste, adding more sugar or lime juice if desired
Garnish with a slice of lime, a sprig of mint, and serve