Preheat the oven to 350 degrees and line a baking sheet with parchment paper.
In a large bowl, add the brown sugar, key lime zest, and butter. Beat until this mixture becomes light and fluffy for 1-2 minutes. Scrape down the sides.
Add in the egg and vanilla and beat on low.
Add in the flour, baking powder, and salt and mix until just combined. Do not overmix.
Allow the cookie dough to rest in the fridge while you make the frosting (about 10 minutes)
To make the frosting, beat together the cream cheese and butter until well combined and fluffy. Add in the salt, key lime zest, key lime juice, vanilla, and heavy cream. Beat until combined.
Add in the powdered sugar and mix until smooth.
Remove dough from the fridge, and scoop out 2 tbsp sized balls of dough. Place on the lined cookie sheet 3 inches apart and bake for 9-11 minutes until edges are just slightly golden brown.
Allow cookies to fully cool before frosting them and serving! Garish with slices of key lime and zest if desired!