To create the simple syrup, combine sugar, water, and basil leaves in a small saucepan. Bring to a simmer over medium heat, stirring constantly until sugar dissolves. Remove from heat and allow to steep for 10 minutes. Strain and cool completely before using.
To create the cocktail, add basil lemon simple syrup, vodka, and lemon juice to a shaker filled with ice. Shake well.
Strain into a cocktail glass filled with ice. Top with club soda and garnish as desired.