Iced Mint Aguas Frescas

In a medium saucepan, combine the sugar, honey and water and bring to a boil, stirring until the sugar is dissolved. Remove from the heat. Add the ginger and half of the mint leaves and let stand until cooled, about 1 hour. Strain the liquid into a large pitcher, pressing hard on the ginger and mint leaves to extract as much of the liquid as possible; discard the solids. Refrigerate until chilled, about 30 minutes. Add the remaining mint leaves, the lemon juice and the lemon slices to the pitcher. Stir in the sparkling water and serve in tall glasses over ice.