Slice two of the peaches for garnish and chop the remaining two peaches.
Place the chopped peaches in a muddler or cocktail shaker and add the sugar and rum.
Muddle the peach, sugar and rum together until well combined and the sugar has dissolved.
You can either strain with a cocktail shaker or directly pour the peach-infused rum evenly into your two serving glasses filled with ice, mint, and peaches.
Garnish with additional peaches.
Add a splash of club soda, as desired.
Notes
To replace the sugar with simple syrup, use 1 teaspoon of syrup for every 2 teaspoons of sugar.