First, make your basil simple syrup. Add ½ cup water, ½ cup sugar, and 2 tablespoons of basil to a small saucepan. Heat up to a boil and stir constantly for about 5 minutes, then remove from heat and let cool.
In a medium bowl, smash or muddle your strawberries down into a juicy pulp.
Mix the strawberry pulp, the rum, and the simple syrup in a cocktail shaker and shake hard for a few minutes.
Pour over ice and garnish with fresh strawberries.