To make the basil simple syrup, add sugar and water to a saucepan. Bring the mixture to a gentle boil. Add the fresh basil, and, using a wooden spoon, break apart the basil to release its oils into the sugar mixture. Continue to cook for 2 minutes. Remove from the heat and allow the mixture to rest for 30 minutes. Strain and transfer to an airtight container. The syrup will stay fresh for up to 1 month in the refrigerator.

To make the gin fizz, add gin, peach liqueur, peach slices, basil, and basil simple syrup to a glass. Muddle to combine. Add ice to the glass and top with peach nectar and club soda. Stir to combine. Garnish with basil and a peach slice.