Rinse the mint and pick enough leaves to firmly fill 1 cup; set the sprigs reserved for garnish aside.
Bring 8 cups of water to a boil in a pot. Remove from heat, add the black tea bags and the 1 cup mint leaves, cover, and steep for 5 minutes.
Lift out and discard the tea bags without squeezing to avoid bitterness. Let the mint continue steeping for 5 minutes more, then strain the tea into a 2-quart pitcher and discard the mint.
Make a simple syrup: In a small saucepan, combine 1 cup water and the sugar. Bring to a simmer over medium heat, stirring until the sugar dissolves, 2–3 minutes. Remove from heat and cool 5 minutes.
Stir the warm simple syrup into the mint tea. Refrigerate until thoroughly chilled, about 2 hours, or until cold to the touch.
Serve the mint iced tea over ice cubes. Garnish each glass with a fresh mint sprig and a lemon slice.