In a cocktail shaker, muddle the grapefruit wedges if using, or add the grapefruit juice, simple syrup, and mint leaves together to release the grapefruit juice and the mint's essential oils.

Add the vodka (or your preferred spirit) and fresh lime juice to the shaker.

Fill the shaker with ice and shake the mixture well until chilled and combined.

Double-strain the cocktail into a rocks glass filled with fresh ice, using a fine-mesh strainer to remove any pulp or mint leaves.

Optionally, garnish with a mint sprig and a grapefruit slice before serving.