Preheat grill to medium-high heat. Brush the cut sides of the peach halves with olive oil.
Grill peaches cut-side down for 3-5 minutes, or until grill marks appear and peaches are slightly softened. Remove from grill and let cool slightly.
While peaches are cooling, bring water to a boil in a saucepan. Remove from heat and add tea bags. Steep for 5 minutes, then remove tea bags.
Stir in granulated sugar until dissolved. Let the tea cool to room temperature.
Once the grilled peaches have cooled enough to handle, roughly chop them. You can discard the skins if you prefer.
In a large pitcher, combine the cooled tea, peach nectar, and chopped grilled peaches. Stir well.
Chill the iced tea in the refrigerator for at least 30 minutes. Serve over ice, garnished with fresh mint sprigs if desired.
Notes
For an extra peachy flavor, you can muddle some of the grilled peach pieces before adding them to the pitcher. Adjust sugar to your sweetness preference.