Prepare the baking sheet by lining with non-stick baking paper and preheat the oven to 350ºF/180ºC.
Grind the walnuts carefully in the food processor. Be careful not to grind too finely or 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 1 to 2 inches apart on the prepared sheet.
Bake until the cookies are a very pale golden brown all over 15-20 minutes.
Sift the powdered sugar into a large flat bowl and add 4 or 5 hot cookies. With two forks or with your fingers, roll the cookies to coat completely with sugar. Then remove the cookies and set on wire racks to cool. Repeat with the remaining cookies while they are hot.
Sift more powdered sugar over the cookies cooling on the wire rack.
Cool completely then store Norwegian Cookies in an airtight container for up to a week.