Place the strawberries and water in a medium sized saucepan over low heat. Let them simmer gently for about 15-20 minutes or until the strawberries are soft and have lost most of their color. The water should be deep red in color.
Using a fine mesh strainer, strain the strawberry water into a separate pot and discard the strawberries.
Bring the strawberry water up to a boil and simmer until it has reduced by about half (roughly ½ cup).
Add in the sugar and stir until the sugar is completely dissolved. Remove from the heat and let cool completely to room temperature.
Store the syrup in an airtight container in the fridge for up to a month.
Place basil leaves and strawberries into a sturdy glass. Use a muddler to gently crush the basil and strawberries to release the basil oils and juice.
Fill the glass halfway with ice. Pour the rum and simple syrup over the ice and then fill the glass with club soda.
Stir, taste, and add more simple syrup if desired. Garnish with basil and strawberries.