Whip butter and icing sugar together until fluffy. Mix in key Lime juice and vanilla. In a small bowl, mix together flour, corn starch and salt. On low, mix dry ingredients into the butter mixture. Turn the dough onto a slightly floured surface, divide in half and firm each half into logs approximately 1 inch in diameter. Wrap each log with parchment paper and refrigerate for about 1 hour. Preheat oven to 325F. Remove logs from refrigerator, unwrap and slice into 1/4 inch discs. Place on a baking sheet and bake 10-12 minutes. Place on a wire rack to cool slightly. While still a little warm, dust each cookie with icing sugar and place back on the wire rack to cool completely.