In a food processor, pulse together the nuts, flour, cornmeal, and salt until finely ground and smooth.
Using a hand-held or stand mixer, beat together the butter and 1/2 cup powdered sugar in a medium bowl until light and creamy. Add the lemon juice, 1 teaspoon zest, and vanilla and beat to combine. With the mixer on low speed, add the dry ingredients in 3 batches until just combined; be careful not to over-mix. Chill the dough in the refrigerator for 30 minutes.
In a shallow bowl, combine the remaining sugar with remaining zest. Set aside.
Preheat the oven to 350 degrees F.
Roll the dough into 1 1/2-inch balls. Transfer the dough onto cookie sheets and bake until firm and very pale golden, about 12 to 15 minutes.
While the cookies are still warm, roll each cookie in the sugar mixture. To achieve a solid coating, roll each of the cookies a second time in the sugar mixture.
Recipe courtesy of Giada De Laurentiis