Mix ginger, sugar and water in a saucepan and bring to a slow simmer. Reduce mixture by 50 percent until a syrupy consistency is reached. Keep in mind that the syrup will thicken as it cools. Strain warm syrup. Allow to cool.
In a tall glass of ice, add mint sprig in a ratio of 1 part ginger syrup to 7 parts soda. Squeeze lime wedge and add to drink. Use more syrup if desired. Stir and enjoy