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Cream together the butter and the sugar.
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Mix in the flour, salt, ground walnuts and vanilla and blend until just incorporated.
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Form the dough into a disc, wrap in plastic wrap and chill for at least one hour or overnight.
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Preheat the oven to 325 degrees.
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Portion the dough into 30 level tablespoons and then roll each into a ball.
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Place the balls on a parchment lined sheet pan, about an inch apart. Chill in the refrigerator for 15 mins before baking.
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Bake until golden, about 20 mins, rotating the pan once.
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Remove the pan from the oven and let the cookies cool on the pan for about 5 mins.
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Place the confectioners sugar in a bowl and toss the warm cookies into the sugar a few at a time until coated.
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After all the cookies are sugared, toss them a second time in the confectioners sugar.
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Enjoy immediately or store in an airtight container for 2-3 days.