Preheat oven to 350 degrees F. In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add the granulated sugar. Beat until combined, scraping side of bowl occasionally. Beat in the 2 teaspoons lime peel, 1/4 cup lime juice, and 1 teaspoon vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour and the nuts. Divide dough in half.
On a lightly floured surface roll half of the dough at a time until 1/4 inch thick. To roll, start from the center and push dough out toward the edges until it is a uniform thickness. Using 1- to 2-inch cookie cutters, cut out dough. Place cutouts 1 inch apart on ungreased cookie sheets.
Bake for 8 to 10 minutes or until edges are light brown. Transfer to a wire rack and let cool.
For frosting, in a medium mixing bowl combine cream cheese, powdered sugar, the 1 tablespoon lime juice, and 1 teaspoon vanilla. Beat with an electric mixer on medium speed until smooth. Spread frosting on cookies. If desired, sprinkle with additional lime peel.