To make the basil syrup

1) Place sugar, water, and basil in small pot.Gently boil until the sugar has dissolved, about 8 minutes.Take off heat and strain out the basil.Chill.To make the sherbet: Use a blender or immersion blender to puree the strawberries, milk, basil syrup, lime juice, and lime zest together.Churn in ice cream maker according to manufacturer's directions.Note: This doesn't freeze particularly well, so if you do freeze it, you may want to take out the sherbet 20 minutes before you serve.