Cut the ends off the lime and slice across to give you 1cm slices.
Dust both sides of the lime slices with sugar and grill or BBQ over high heat, turning once, until lightly caramelized. Reserve a slice for serving on the side of the glass.
Muddle the lime wheels and ginger with the 2 tablespoons of sugar. Fill the glass with ice, add the cachaça and soda, if using, and stir well.