Preheat the oven to 400°. Line sheet pans with parchment paper or silicone baking mats.
Combine the butter, sugar and vanilla in the bowl of a food processor (or in a mixing bowl with a mixer). Add the flour and salt. Pulse until coarse crumbs forms. Shape the dough into walnut-sized balls, pressing to pack your own snowball cookies.
Place the dough balls on an ungreased cookie sheet or one lined with a silpat baking mat. Bake until set about 9 minutes. Do not brown. Roll the warm cookies in powdered sugar.
Store in an airtight container. To freeze, layer the cookies between sheets of parchment or waxed paper.Nutritional values are approximate and based on 1 cookie.