Preheat your oven to 350 degrees F and spray your cookie sheets with nonstick spray.
In a large mixing bowl, whisk together the butter, sugar and eggs until creamy (looks like really creamy butter). Add the lime juice and grated lime peel.
In another bowl, whisk together the dry ingredients.
Mix the dry ingredients into the wet ingredients until moistened.
For best results refrigerate the dough for about 1 hour, or put in the freezer for about 20 minutes.
Form the dough into balls and place on your prepared cookie sheet.
Bake for 8-10 minutes. Allow to rest on cookie sheet for 2 minutes.
Key Lime Icing:
In a small bowl, mix powdered sugar, key lime juice and key zest in a bowl.
Add in milk and continue stirring until mixed well and it's a nice thick consistency, yet pourable. If you need to add a tiny bit more milk, it's okay.
Scoop frosting onto cookies and use the back of a spoon to smooth it on.
Allow to set up on a cookie rack. Store in an airtight container for up to 1 week.