In a cocktail shaker, combine strawberries, simple syrup, and lime juice and muddle until strawberries are completely dissolved. Add mint leaves and gently tap 5 times with muddler. (Do not over-muddle mint or it will taste bitter and muddy.) Add vodka to shaker and fill 2/3 full with ice. Shake until well chilled, about 15 seconds.
Fill a Collins glass with ice and add club soda. Fine-strain cocktail into glass and stir gently. Garnish with lime, mint, or strawberry, if desired.