Finely mince the fresh tarragon.
Combine sugar, powdered sugar, baking soda, minced tarragon, lime zest, and gold shimmer powder (if using) in a blender or food processor. Pulse, shaking or stirring often, until the sugar becomes fine in texture and the tarragon and lime zest are well integrated.
Transfer the sugar mixture to a medium sized bowl and stir in the green gel food coloring. Add water, a splash at a time, until the mixture is damp, but not wet. You want it to be able to come together, but the drier the better.
Use a tablespoon to mold the cocktail fizzers into half spheres. Transfer to a baking sheet or plate and allow to air dry for at least 4 hours or overnight. OR: Spread the baking soda mixture out on a baking sheet and allow to air dry.