From David Lebovitz
Garnish: strawberries, lime wheel
Strawberry-infused vermouth: pour the vermouth in a clean jar. Add the strawberries, cover, and shake gently to encourage the strawberries to lend their flavor to the vermouth. Let stand 24 hours at room temperature out of direct sunlight, giving it a shake every so often.
In a cocktail shaker, muddle the strawberries and simple syrup.
Add remaining ingredients, then fill half with ice.
Shake until well-chilled, about 15 to 20 seconds.
Pour all into a glass and garnish.