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Position a rack in the middle of the oven.
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Preheat the oven to 325°.
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Trace nine 3 1/2" circles on each of two pieces of parchment paper the size of your baking sheets, leaving 1" between the circles.
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Line the baking sheets with the paper, marked side down.
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In a large bowl, using an electric mixer on low speed, beat the butter, sugar, salt, lemon zest, and vanilla until smoothly blended, about 1 minute.
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Stop the mixer and scrape down the sides of the bowl as needed during mixing.
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Add the flour and mix until the dough forms small crumbs, varying in size from fine crumbs to about 1/4" in size.
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Use a 1/4 cup measuring cup to scoop up 1/4 cup crumbs and spread them in one of the marked circles.
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Pat the crumbs gently to fill the circle, but do not pack them tightly.
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Sprinkle about 1 tbls of loose crumbs over the top. To produce the crumbly looking top.
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Repeat to make a total of 18 cookies.
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Bake the cookies one sheet at a time until the bottoms and edges are light brown, about 21 minutes.
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The centers of the cookies should still be a lighter pale golden color.
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Cool the cookies for 10 minutes on baking sheets, then use a wide metal spatula to transfer them to a wire rack to cool completely (some crumbs may fall off the edges) do not try to transfer the cookies before 10 minutes -- they must cool and firm slightly so they will not break.
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Dust the cooled cookies lightly with powdered sugar.
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The cookies can be stored in a tightly covered container at room temperature for up to 3 days.