Bring water to a boil; place mint and tea bags into a large pitcher or bowl. Pour boiling water carefully over mint and tea bags; steep, covered, for 5 minutes. Strain to remove mint and discard tea bags. Stir in honey. Cool slightly.

Pour tea mixture into an 8-by-8-inch metal pan. Cover and place pan in freezer for 1 hour. Remove pan from freezer and scrape mixture with a fork, crushing any lumps. Freeze an additional 20 minutes; remove and scrape. Repeat every 20 minutes until mixture is fluffy.