Preheat oven to 325 degrees and line a baking sheet with parchment paper. In a large bowl mix butter and powdered sugar together until sugar is completely dissolved and no lumps remain. Add vanilla, salt and lime zest then stir until combined.
Sift flour and baking powder over butter mixture and mix just until dry ingredients are mixed into butter and no dry spots remain—the dough will still look a bit dry and will not yet have formed a cohesive mass.
Add lime juice and mix only until the dough comes together—don’t overwork the dough or cookies will become tough. Scoop approximately 2 tsp of dough and roll into a 1" ball. Place on baking sheet and repeat with all remaining cookie dough—they’ll spread in the oven so there’s no need to press them down.
Bake 14–16 minutes or until the cookies become just slightly golden brown around the edges. Remove from oven and carefully transfer to a cooling rack, as they’re quite fragile when warm.
When the cookies have cooled a bit but are still slightly warm, add approximately a cup of powdered sugar to a small bowl. Gently roll the cookies in the sugar to coat then allow them to cool completely on the rack.
Notes
Sift any unused powdered sugar to remove cookie crumbs and save for later use.