Line a baking sheet with parchment paper and set aside.
In a bowl, combine butter, ½ cup powdered sugar and vanilla extract until very creamy, about 4 minutes. Meanwhile, mix together flours and salt in a small bowl.
Add flour mixture to the butter mixture and mix until just combined.
Scoop cookie dough into approximately 1-inch balls and place on prepared baking sheet. Wrap baking sheet in plastic wrap and refrigerate cookie dough for at least 2 hours or overnight.
When ready to bake cookies, preheat oven to 375°F and line baking sheets with parchment paper. Place remaining 2 cups of powdered sugar in a large bowl.
Toss cookies in powdered sugar to coat and place on prepared baking sheets about 1 inch apart. Bake until the bottoms are lightly browned, 10–12 minutes. Immediately and carefully roll hot cookies in powdered sugar and transfer to a rack to cool completely.
Toss cookies a third time in powdered sugar once completely cooled.
