Make the purée: In a small bowl or muddler cup, combine the strawberries, basil leaves, and 1 tablespoon of simple syrup. Muddle until the strawberries are broken down and the basil is fragrant. Press through a fine mesh strainer if you want a smoother cocktail, or leave it rustic.
Build the cocktail: In a cocktail shaker, combine the vodka, strawberry basil purée, lemon juice, and simple syrup with ice. Shake vigorously until well chilled, about 15 seconds.
Strain into two coupe glasses.
Garnish each with a fresh basil leaf and a strawberry slice on the rim. Serve immediately.