Coat the tarragon sprigs in Chartreuse and heat carefully over an open flame for about 15 seconds each.
Set one ┬"smoked┬" tarragon sprig aside and muddle the second in a shaker with the Honeydew Honey Syrup.
Add the gin, lemon juice, bitters and 2 tsp.
Yellow Chartreuse, and fill with ice.
Shake vigorously and fine-strain into a fluted pilsner glass filled with fresh ice.
Garnish with the reserved ┬"smoked┬" tarragon sprig.