In a large pot bring 6 cups of water to a boil over high heat. Stir in the licorice and cinnamon; lower to a simmer, partially cover the pot, and simmer for 10 minutes. Remove from heat, stir in peppermint, cover, and steep for 10 minutes.
Meanwhile, place a large strainer lined with cheesecloth or a damp paper towel over another pot or heatproof bowl. Strain tea, pressing on herbs to extract all liquid. Stir in honey until dissolved and let cool completely, about 1 hour. Fill four tall glasses with ice. Pour tea over ice and garnish each glass with a mint sprig, if desired. Serve immediately.