To make the basil simple syrup combine 1 cup of sugar with 1 cup of water and a handful of fresh basil leaves in a saucepan over medium heat. Smash the leaves a bit while stirring the mixture to dissolve the sugar. Simmer for 5 minutes then turn off heat. Let cool for about an hour for the mixture to infuse with the basil. Strain and cool completely before using. This can be made ahead of time and kept in the fridge for up to 2 weeks. I use a Mason jar.
For the Cocktail
In a cocktail shaker, muddle several chunks of the diced pineapple with 3-4 leaves of basil.
Add the vodka, simple syrup, pineapple juice and lemon juice to the shaker with a few cubes of ice. Put the lid on the shaker, and shake vigorously.
Fill a tall collins glass or hurricane glass halfway with ice.
Pour mixture over ice and top with about 1 oz per glass of club soda, to add some sparkle and fizz.
Garnish with a few pineapple chunks, a sprig of fresh basil and a pretty straw!