Place the granulated sugar on a small plate. Rub a lemon wedge around the rim of a martini or coupe glass and dip the rim into the sugar. Set aside.
Remove the hulls from the strawberries and slice them. Place the slices in a small bowl. Use a muddler or the back of a spoon to release the juice, then strain through a fine mesh sieve. Discard the solids.
In a cocktail shaker, add the strawberry purée, vodka, lemon juice, triple sec, simple syrup (if using), and a handful of ice cubes. Shake well.
Strain the cocktail into the prepared glass. Garnish with a strawberry slice and a lemon wedge if desired. Enjoy!