Bring 1 liter (approximately 4 1/4 cups) water to a boil. Add tea leaves and let steep about 3 minutes. Pour tea through a fine sieve into a shallow dish. Rinse mint sprigs (reserving up to six for garnish) and add to tea. Let cool.
Remove mint from tea and pour into a shallow metal tray. Freeze 6-8 hours, stirring with a fork after about 2 hours to prevent large ice crystals from forming. Thereafter, stir mixture every hour.
Divide tea granita among glasses, top with peach liqueur and serve garnished with remaining mint sprigs and chocolate mints.