Place the strawberries, basil leaves, and simple syrup into a cocktail shaker.
Muddle the ingredients thoroughly to express the oils from the basil and the juice from the strawberries.
Add the gin and fresh lemon juice to the shaker.
Fill the shaker with ice and shake vigorously for approximately 15 seconds until well-chilled.
Double strain the mixture through a fine-mesh sieve into a rocks glass filled with fresh ice.
Top with a splash of club soda if a lighter effervescence is desired.
Garnish with a fresh basil sprig and serve immediately.