Preheat the oven to 350 degrees. Line your baking sheet(s) with parchment and set aside.
In the bowl of a stand mixer or using an electric hand mixer, combine the 1/3 cup softened butter and 1 cup sugar. Cream until combined.
Add in 1 egg and combine. Then add in the 1 tsp zest, 1/4 cup juice, and 1/2 tsp vanilla and continue to mix thoroughly.
Add in the 2 1/2 cups flour, 1/2 tsp salt, 1/4 tsp baking soda, and 1/4 tsp baking powder. Mix well. Scrape down the sides and mix again.
Scoop out the dough using a #24 cookie dough scoop (about 2 ½ Tbsp for each ball of cookie dough). Place the cookie dough on your prepared baking sheets and press down on top of the cookie dough to flatten it to about ½” thick.
Bake the cookies for 10 minutes, until the bottom is beginning to brown and the edges have set. Do not worry if the top has browned at all as this will result in overbaking.
Remove the cookies from the oven and immediately transfer them to a cooling rack.
Next, make the glaze. In a small bowl, combine the 1 tbsp key lime juice and 1/2 cup powdered sugar. The mixture should be a drizzling consistency. Add more juice if needed to reach the desired consistency.
Once the cookies have cooled, drizzle the glaze over the cookies.
Immediately sprinkle with the additional zest, if using.