Place tea bags in the bottom of a large pitcher and cover with boiling water. Let steep for 30 minutes.
While tea is steeping, make the mint infused simple syrup by pouring boiling water over sugar and mint sprigs. Stir with a fork to dissolve sugar and gently press on mint leaves to release flavor and natural oils. Allow syrup to cool, about 15 minutes.
Once tea has steeped, remove tea bags and add 3 quarts of cold water. Strain the simple syrup to remove the mint sprigs and add to the tea.
Juice half of the lemon and add to the tea. Slice the remaining half for garnish.
To serve, fill glasses with ice and fill ⅔ of the way with tea. Top each glass off with a splash of club soda and garnish with a lemon slice and extra mint sprigs.
For easy removal of the tea bags, tie all 12 together in a knot before adding to the pitcher. Want to kick this recipe up a notch? Splash in a bit of vodka before serving. Sweet tea or citron flavors would be great.