In a small sauce pot, combine sugar and water and bring just to a boil. Add basil leaves and allow to steep in refrigerator until cool. While syrup is cooling, place a medium/large baking dish in your freezer to chill.
In a blender, blend together strawberries, basil syrup, lime zest and lime juice until smooth. Pour into chilled baking dish, place back in freezer, and allow to freeze for 30 minutes.
Using a fork, gently scrape down ice crystals starting to form. Continue to freeze for 2 hours, scraping every 45 min or so until a flaked ice like texture. Scoop into a small cup and enjoy!