Preheat the oven to 350, and line a small baking sheet with parchment paper.
Crush the graham crackers to get 1/4 cup of crumbs, and set aside.
In a small bowl, beat together with an electric mixer the sugar and Key lime zest for about 30 seconds.
Next, slice the cold butter into about 16 pieces, and then add it to the bowl.
Beat the butter into the sugar until creamy and fluffy, about 45 seconds. Add the egg and beat just until combined.
Next, sprinkle the flour, salt and graham crackers evenly over the surface, and beat until just combined. The dough will be crumbly, use the warmth of your hands to bring it together.
Have the powdered sugar ready in a shallow dish.
Scoop out 12 balls of dough, and roll lightly in powdered sugar before placing on the baking sheet, evenly spaced. Reserve the remaining powdered sugar
Bake for 15 minutes; the cookies will not turn brown. Do not over bake.
While the cookies are still warm, roll them each in powdered sugar again.