Prepare canner and wash/sterilize 8 half-pint mason jars. Keep jars in hot (not boiling) water until ready to use.
In a small bowl, whisk together ¼ cup of sugar and pectin. In a separate bowl, measure out remaining 4 ¼ cups of sugar and set aside.
Wash blueberries and discard stems. Place in a blender or food processor. Cover and pulse to evenly chop. Do not liquefy. Transfer all but ¼ cup of blueberries into an 8-quart saucepan.
Add basil, lemon juice, and water to remaining berries in food processor. Pulse until well blended and no large chunks of berries or basil remain. Add to blueberries in saucepan.
Stir pectin mixture into blueberries, and cook over medium-high heat until mixture reaches a full roiling boil that cannot be stirred down.
Quickly stir in remaining sugar. Return to a boil, and boil for exactly 1 minute, stirring constantly. Remove from heat. Skim off any foam.
Ladle hot jam into jars, leaving ⅛-inch of headspace. Wipe jar rims and threads. Screw on lids and rings.
Process in a boiling water bath for 10 minutes. Remove from water and let cool completely, 12 to 24 hours. Check seals. Any unsealed jars should be refrigerated and used within 3 weeks.
