In a saucepan, bring 4 cups of water to a boil. Remove from heat, and add in tea bags and 3 mint sprigs. Cover and let steep for about 15-20 minutes. If you want a stronger tea flavor, steep for about 30-45 minutes.
Remove the tea bags and mint, and stir in honey. In a large pitcher, add green tea, about 1-2 cups of ice, 2 cups cold water, and green tea mixture. Serve over ice and garnish with more fresh mint.