Separate the eggs. Place the egg whites in a small bowl. Set aside. Chop the walnuts. Cut the butter into small cubes.
Note: We will use the egg yolks for the dough and the egg whites to decorate the cookie.
In a large bowl, place flour, powdered sugar, butter, and lemon zest. Work the butter into the flour and sugar until you obtain a sandy mixture.
Add the egg yolk and vanilla, and mix until you obtain a smooth, nonsticky dough.
Shape the dough into a ball, wrap it in foil and place it in the refrigerator for at least 30 minutes to an hour.
Remove the dough from the refrigerator and place it on a clean surface.
Preheat oven to 350F. Line a cookie dough with parchment paper and set it aside.
Beat the egg whites with a fork. In a different bowl, place the coarsely chopped walnuts.
Take small pieces of dough and shape them into 1 inch balls. Dip them into the egg whites, then roll them on the chopped walnuts, pressing gently to help the walnuts stick to the cookie.
Place the cookies 1 inch apart on the cookie tray. Bake until edges are lightly browned, and cookies are set for about 25 minutes.
Remove the baking tray from the oven and dust cookies with powdered sugar.
Place the cookies on a metal rack to cool.