Place the basil and sugar into cocktail shaker. Using a muddler, crush the basil leaves and mash them into the sugar to break them up.

Add the peach portion and crush. Add the lime juice, simple syrup, rum and ice. Place the top onto the shaker and shake it until the sides start to chill.

Fill a glass with crushed ice. Strain the drink into the glass and serve with a basil leave.