Prepare the Basic Simple Syrup as directed, adding half of the sliced ginger before bringing it to a boil. Remove from the heat and let steep for 30 minutes. Strain the ginger syrup into a large measuring cup.
In a large saucepan, combine the remaining sliced ginger with the cold water and bring to a boil. Remove from the heat and add the tea bags. Let steep for 6 minutes. Strain the tea into a large bowl and let cool to room temperature, then refrigerate until chilled.
Pour the tea into a large pitcher and stir in 1 cup of the ginger syrup, or more to taste; refrigerate the rest for later use. Serve in tall glasses over ice, garnished with lemon wedges.
The iced tea can be refrigerated in a covered pitcher for up to 2 days.