Combine sugar and water in a small saucepan; bring to a boil. Cook 1 minute or until sugar dissolves. Cool sugar syrup completely.
Cook lemon verbena leaves in boiling water 1 minute. Drain and plunge into ice water; drain.
Combine sugar syrup and verbena leaves in a blender; process until smooth. Cover and chill overnight. Strain sugar syrup through a fine sieve into a bowl. Place 2/3 cup ice into each of 6 tall glasses; add 1 cup brewed tea and 2 tablespoons sugar syrup to each serving, stirring to combine. Garnish with mint leaves and lemon wedges, if desired.