Make the ginger syrup: In a small saucepan, combine the fresh ginger, agave, and water. Bring to a boil then reduce to a simmer and cook for 35 minutes. Careful not to cook at too high of a temperature or the ginger will burn. Set aside to cool.Make the spritzers: Fill two 16-ounce glasses with ice. Add 2 tablespoons of ginger syrup in each and juice of 1/2 lemon in each. Distribute fresh mint evenly and fill each glass with sparkling water. Serve immediately and enjoy!