Preheat oven to 350 degrees Fahrenheit. Line 2 cookie sheets with parchment paper and set aside.
Sift flour, confectioners sugar, and sea salt into a large mixing bowl. Set aside.
Cream together the butter, shortening, and vanilla extract.
On medium-low speed, mix in the flour mixture and walnuts. Beat until dough just starts coming together in a heap.
Using your hands, portion out the dough and make small balls. You can fit up to 20 of them on a cookie sheet; they do no spread much.
Bake for 15 minutes, or until lightly browned around the edges.
Remove immediately to a wire rack to cool.
Once cooled a bit, drop cookies, a few at a time, into a zip top bag filled with the other 1/2 cup confectioners sugar. Shake around a bit to coat, then return to wire rack to cool completely.