Around the world, these buttery, nutty cookies go by lots of different names: Mexican Wedding Cookies, Russian Tea Cakes, Sand Tarts, Polvorones, and more.
Adjust oven rack to middle position and heat oven to 325 degrees. Line rimmed baking sheet with parchment paper.
Place walnuts in large zipper-lock plastic bag and seal, removing as much air as possible from bag. Use rolling pin to gently pound walnuts into very small pieces.
In medium bowl, whisk together pounded walnuts, flour, and salt.
Add softened butter and sugar to bowl of stand mixer (or large bowl if using handheld mixer). If using stand mixer, lock bowl into place and attach paddle to stand mixer. Start mixer on medium-high speed and beat until pale and fluffy, 3 to 4 minutes. Stop mixer and use rubber spatula to scrape down sides of bowl.
Add vanilla and flour mixture. Start mixer on low speed and mix until combined, about 45 seconds. Stop mixer. Remove bowl from stand mixer, if using. Use rubber spatula to scrape down sides of bowl and stir in any remaining dry flour.
Use your hands to roll dough into 24 balls (about 1 tablespoon each). Place dough balls on parchment-lined baking sheet, leaving space between balls.
Place baking sheet in oven. Bake cookies until tops are pale golden and bottoms are just beginning to brown, about 18 minutes.
Use oven mitts to remove baking sheet from oven (ask an adult for help). Place baking sheet on cooling rack and let cookies cool completely on baking sheet, about 20 minutes.
Mexican Wedding Cakes, Nut Crescents, Viennese Crescents, Butterballs, Russian Tea Cakes, Swedish Tea Cakes, Italian Butter Nuts, Southern Pecan Butterballs, Snowdrops, Viennese Sugar Balls, Sand Tarts, and Snowballs… These are all names for the same type of cookie—this one! People have been baking them all over the world for generations. Light, buttery, nutty, and tender, these cookies are delicious by any name.