In a large mixing bowl, beat the softened 8 ounces unsalted butter and 1/2 cup powdered sugar until creamy. Stir in the 1 1/4 teaspoons vanilla extract.
In a separate bowl, whisk together the 2 cups all-purpose flour, 1/4 teaspoon salt, and 1 teaspoon baking powder.
Gradually add the flour mixture to the creamed butter mixture, mixing just until combined.
Fold in the 2/3 cup chopped walnuts.
Shape the dough into a ball, wrap it in plastic wrap, and chill in the refrigerator for 1 hour.
Remove the dough from the fridge and preheat the oven to 375°F. Unwrap the dough and roll it out on a lightly floured surface to your desired thickness. Cut into shapes.
Place the cut cookies on an ungreased cookie sheet and bake at 375°F for 10–12 minutes, until the cookies are firm but not browned.
Remove the cookies from the oven and, while still warm, roll them in additional powdered sugar. Allow to cool before serving.