In a large bowl, using a hand or stand mixer, cream the butter and sugar until combined and fluffy. Add the eggs and vanilla. Mix until well combined. Set it aside.
In another bowl, whisk the flour, salt, and baking powder. Add the flour mixture into the wet mixture and mix until a cookie dough has formed.
Using a ¼ cup measuring cup, scoop dough out and place onto ungreased cookie sheet. Using the bottom of a glass or measuring cup, press into the dough to flatten before baking.
Bake for 10-11 minutes, until the centers are no longer shiny. Cool on the cookie sheet for 5 minutes and then move to a cooling rack. Cool completely before frosting.
Frosting
In a large bowl, using a hand or stand mixer, mix the powdered sugar and butter until frosting consistency has formed. (If the frosting has trouble coming together, add 1 tbsp of the coconut cream and continue mixing.)
Add the remaining coconut cream and extract, mix until well combined.
Frost each cookie and set aside to form a cast. Cover cookies and chill until ready to eat. When ready to eat, squeeze a wedge of lime on the cookie for that twisted sugar lime coconut taste.