For the Strawberry Syrup: In a small saucepan, combine strawberries, sugar, and lemon rind. Cover and let stand, stirring occasionally, for 1 hour at room temperature.
Once the sugar has dissolved and the strawberries have released their liquid, bring the mixture to a simmer over medium heat. Cook, stirring gently, until the berries are tender, about 3 minutes.
Using a slotted spoon, transfer the cooked strawberries to a pint jar. Continue simmering the syrup until it thickens to a syrupy consistency, about 2 minutes. Discard lemon peel and pour syrup over berries. Let cool to room temperature, then store in the fridge for up to 1 month.
To Make One Cocktail: In a cocktail shaker, thoroughly muddle 4 hulled strawberries with the lemon. Add the strawberry syrup, balsamic, and bourbon, then fill shaker with ice and close shaker.
Shake vigorously until well chilled, about 15 seconds. Using both a cocktail strainer and a fine mesh strainer, strain the cocktail into a glass. Garnish with a strawberry.
