Combine agave nectar, basil and water in a saucepan over medium heat. Cook over medium heat, stirring frequently, until flavors blend - about 10 minutes.
Strain and set aside to cool slightly - you want it to be warm, just not boiling. Once cooled, combine your liquid and frozen raspberries in your blender or food processor and pulse until the mixture is very smooth.
Strain the raspberry mixture through a fine mesh strainer to get out all seeds and remaining solids. You'll need to work a little here, it works well to push the mixture through with a rubber spatula.
Mixture should be cool from the frozen raspberries, if it is still warm put in the fridge to cool for an hour.
Once the mixture is cooled, start up your ice cream maker and add in the mixture.
Once your sorbet becomes the consistencey of soft serve, you're done.
Serve immediately, or freeze overnight in an airtight container for a more solid sorbet.
Leftovers can be stored int the freezer for about a week.
To quickly cool my agave/basil liquid - I added the syrup to a pyrex measuring cup, set it in the sink and filled the sink with cold water. This brings it to a lower temperature fast.
Adding the warm liquid in with the frozen raspberries should result in an already cold mixture you can add right to your ice cream maker.
If you don't have an ice cream maker - let the mixture cool completely (if it is in any way warmish) in the fridge, then transfer to the freezer in an shallow container. A metal bread pan would be perfect. Cover with cling wrap to keep air off (and frost) and freeze. Push the cling wrap into the pan so it is just barely touching the surface of the sorbet mixture. You'll still have sorbet, it just won't be as creamy.