Preheat the oven to 350 degrees F (175 degrees C).
Cream butter and vanilla together in a medium bowl with an electric mixer until smooth, 2 to 3 minutes.
Whisk flour and 6 tablespoons powdered sugar together in separate bowl. Add to the butter mixture and stir until just blended. Add walnuts and mix until incorporated; mixture may be crumbly.
Take small scoops of dough and roll between your hands into 1-inch balls. Place balls 2 inches apart on ungreased cookie sheets.
Bake in the preheated oven until edges are just turning golden, about 12 minutes.
Remove from the oven and transfer to a wire rack to cool for 15 minutes.
Place remaining 1/3 cup powdered sugar in a small bowl. Roll cooled cookies in the powdered sugar once or twice.
