Make the syrup: add water, sugar, sliced strawberries, and torn basil leaves into a small pot. Cook over low heat until the sugar is dissolved. While the syrup is coming to a boil, muddle (mash) the strawberries using a muddler or a wooden spoon to break up the strawberries and infuse the syrup with strawberry and basil flavor. Strain the syrup through a fine-mesh strainer, discard the strawberry pulp and basil leaves. Leave to cool.
Make the drink: add simple syrup, lemon juice, rum, 3 sliced strawberries, and 2 basil leaves into a short drink glass. Muddle (mash) the strawberries and basil just slightly to break them up and release the flavor.
Top with sparkling water, ice cubes, stir to combine. Add the remaining 1 strawberry (sliced) and 2 basil leaves for decoration.
Adjust the sweet-sour flavors if necessary by adding more lemon juice if the drink is too sweet or more syrup if the drink is too sour.
Enjoy!