Preheat the oven to 350 degrees Fahrenheit. Line 2 bakingsheets with parchment paper. Set aside
In the bowl of your electric mixer (or with a hand mixer), cream the butter and sugar until light and fluffy (about 2 minutes). Beat in the vanilla extract. Add the remaining flour and salt and beat until combined. Stir in the nuts. Cover and refrigerate the dough for about 1 hour or until firm.
Form the dough into 1 inch (2.54 cm) balls and place them 2 inches (5 cm) apart on the prepared baking sheets. Bake for about 12-15 minutes, or until the edges of the cookies start to brown. (Mine needed 12 minutes) Remove from oven and pleace on a wire rack to cool for about 5 minutes.
Meanwhile, line another baking pan or tray with parchment or wax paper. Sprinkel about 1/2 cup of the confectioner's sugar on the bottom of the pan and then place the slightly cooled cookies on top of the sugar. Place the remaining 1/2 cup of sugar in a fine strainer or sieve and then sprinkle the tops of the cookies (or you can just roll the cookies in the sugar, that's what I did).
Store in an airtight container. Makes about 3 dozen cookies.