Bring water to a simmer in a medium saucepan over medium-high heat (don’t let it boil), about 5 minutes. Add the green tea, cover partially, and let steep until the flavor is stronger than desired but not bitter, about 15 to 20 minutes.
Once the tea has steeped, discard the tea, add cinnamon, cardamom, and mint (minus about 6 to 8 stems, you’ll want to reserve for garnish) and let cool to room temperature, about 1 hour. Add the ice to the tea, then stir in the passion fruit juice and honey. Place in the refrigerator to cool completely, about 2 hours.TIP: The tea can be made through this step up to two days ahead. Discard the cinnamon, cardamom, and mint after it is cool (about 2 hours) and then store refrigerated in an airtight container until ready to use.
Once the tea is cold, discard the cinnamon, cardamom, and mint and stir in the lime juice. Taste and adjust with more lime juice or honey as desired. Serve iced tea over ice and garnish each glass with a sprig of mint.