In your boiling water, add tea bags and a half cup of the fresh berries to Instant Pot® and stir to combine. Add lid and lock into place. Switch the vent to “Sealing” and set the “Manual” setting to 5 minutes.
While the tea is brewing, add the remaining juicy blackberries, basil, honey, and water to a saucepan set over medium heat. Cook, gently pressing on the blackberries to release their juices while continually stirring the mixture to combine, for 4-5 minutes. Once the honey is completely melted and the mixture starts to thicken, remove from heat and set aside.
When cooking time on Instant Pot® is complete, allow pressure to release naturally for 10 minutes, then do a quick release to release any remaining pressure.
Discard tea bags and carefully strain the hot tea mixture with a fine wire-mesh strainer. Pour the reserved liquid into a large, heat-resistant pitcher and sweeten with the blackberry honey simple syrup, to taste. Add fresh lemon juice and stir to combine.
Serve immediately in a glass pitcher with ice cubes and fresh blackberries. Garnish with a sprig of fresh basil. Enjoy!