Prepare the cookie sheet by lining with non-stick parchment paper and preheat the oven to 350ºF/180ºC.
Grind the walnuts finely in the food processor. Be careful not to over process because it will create a nut butter. Set aside.
Beat the butter with an electric mixer until smooth and creamy. Add sugar, salt and vanilla and beat for 1 or 2 minutes until smooth and fluffy.
With a wooden spoon stir in the nuts, then stir in the flour until the dough gather into a mass. Knead the dough briefly in the bowl until it comes together.
Divide the dough into 36 equal parts. Roll each into a ball and place on the lined cookie sheet. Allow room for the cookies to puff a little.
Bake until the cookies are a very pale golden brown all over 10-15 minutes.
Allow the cookies to cool for 10 minutes or so then sieve the powdered sugar into a large flat bowl. Use two forks to roll the cookies to coat lightly with sugar. Dust of excess sugar and set on wire racks to cool. Repeat with the remaining cookies.
Sift more powdered sugar over the cookies when cool.
Store Norwegian Cookies in an airtight container for up to a week.