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Preheat oven to 325 degrees F. Line an 8-inch by 8-inch by 2-inch baking pan with parchment paper or heavy-duty aluminum foil, leaving enough parchment paper to overhang on the sides. Set aside.
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To make the shortbread crust, in a large bowl stir together both sugars and the flour. Using a pastry cutter, fork or your fingers; cut cold butter into flour mixture until coarse crumbs are formed. If needed, use your hands to shape dough into a ball.
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Pat the dough into the prepared pan, wet hands with a little bit of water, if needed, to help press dough into the pan. Use a fork to prick the dough all over.
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Bake crust on middle oven rack at 325 degrees F for 30-35 minutes or until the edges are lightly browned and the top is a pale golden color but not brown.
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Meanwhile, prepare lemon curd topping. Place a small strainer over a bowl and set aside.
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Heat a large, heavy saucepan over medium-low heat. Add egg yolks and granulated sugar and cook, whisking constantly, until well blended and pale yellow in color, about 3-4 minutes. Slowly whisk in lemon juice, butter and salt. Cook over medium-low heat, whisking constantly, for 5-6 minutes, or until sauce is thickened and deep yellow in color. Lemon curd must not come to a boil. Lemon curd is ready when it coats the back of a spoon but is still liquid enough to pour.
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When the curd has thickened, pour it at once into the strainer. Using the back of a spoon, press un-til only the coarse residue remains. Discard residue and stir in lemon zest.
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When the shortbread crust is baked, remove from the oven, and lower oven temperature to 300 degrees F. Pour prepared lemon curd on top of the shortbread crust, and return to the 300-degree oven for 10 minutes.
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Allow lemon bars to cool completely in the pan on a wire rack. Once cooled completely, refrigerate the lemon bars in the pan for at least 30 minutes before serving.
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Right before serving, place the powdered sugar in a mesh strainer and tap the strainer with a spoon to sprinkle a thick coating of powder sugar evenly over the lemon curd topping.
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Using the overhanging parchment paper, lift the lemon bars out of the pan and transfer to a cutting board. Using a long, sharp knife, cut into bars; wiping the knife blade with a paper towel after each cut.
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The powdered sugar will start to be absorbed into the lemon curd after several hours, but it can be reapplied again as needed.