Muddle lime wedges and brown sugar in the bottom of a highball glass. Add mint leaves and gently crush with muddler. Half fill the highball glass with crushed ice and add rum. Stir ingredients together ensuring lime wedges and mint leaves blend evenly throughout mixture. Top with crushed ice and repeat stirring process.
As you stir ingredients together the melt water replaces what the soda would have added.
My personal preference adapted from traditional recipe.