In a medium bowl, whisk together flour and baking soda then set aside.
In a large bowl, cream together the butter, sugar and lime zest until light in color. Add in egg, vanilla and salt and beat to combine. Gradually add in flour mixture, stopping to scrape the bowl periodically.
Roll cookie dough into 1” balls then place on parchment covered cookie sheet, leaving 2 inches between cookies.
Bake 15-17 minutes or until edges are slightly golden. Let cookies cool completely before adding icing.
For the icing
For the icing: pour lime juice into a small bowl. Gradually whisk powdered sugar into lime juice until fully incorporated and smooth (no lumps). Spoon icing onto cookies as desired.