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Preheat the oven to 325 degrees F.
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In a medium bowl, mix together the flour, 1/3 cup of confectioners' sugar, and butter until butter is in very small crumbs. Press into the bottom of a 11x7 inch pan.
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Bake for 25 minutes in the preheated oven, or until firm and lightly browned.
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While the crust is baking, whisk together the eggs, 2/3 cup of confectioners' sugar, lemon juice and lemon zest in a medium bowl. Just before the crust is done, stir in the baking powder. Pour over the crust while it is hot, and return to the oven.
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Bake for another 25 minutes in the preheated oven, until set. When cool dust with remaining confectioners' sugar. Cut into squares.