In a medium saucepan, bring 4 cups of water to a boil. Once boiling, remove from heat and add the green tea bags. Let steep for 5 minutes, then remove the tea bags and allow the tea to cool to room temperature.

While the tea is cooling, place the honeydew melon cubes and fresh mint leaves in a blender. Blend until smooth.

Strain the blended mixture through a fine mesh sieve into a large pitcher, discarding the solids.

Once the tea has cooled, add it to the pitcher with the honeydew-mint mixture. Stir in the honey until fully dissolved.

Refrigerate the tea for at least 1 hour to chill.

Serve over ice cubes and garnish with mint sprigs and honeydew slices.