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1
Position oven rack in center of oven; preheat oven to 350; grease a 13 x 9 inch baking pan and line it with parchment paper, leaving about 1 inch of paper overhanging the two long sides.
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2
In the bowl of a food processor, combine the flour, brown sugar, powdered sugar, ginger, cinnamon, and salt; process briefly.
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3
Sprinkle the butter on top and pulse until the mixture resembles a coarse meal.
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4
In a small bowl, whisk together the egg and water; slowly pour the egg mixture through the feed tube, pulsing until the mixture begins to hold together (if the mixture does not hold together when pressed between your fingers, pulse in more ice water, 1 teaspoon at a time).
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5
Transfer the mixture to the prepared pan and press evenly onto the bottom of the pan.
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6
Bake for 20 minutes, or until golden.
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7
Remove the pan from the oven and set it on a wire rack to cool slightly; decrease oven temperature to 300.
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8
While the crust is baking, whisk together the eggs and sugar in a bowl, until well combined and pale in color.
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9
Stir in the lemon juice, flour, ginger, and lemon zest.
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10
Pour over the warm crust; return the pan to the oven, and bake for 30 minutes, or until set.
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11
Remove the pan from the oven and set it on a wire rack, allowing it to cool completely.
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12
Remove the squares by grasping and lifting the edges of the parchment; cut into bars.
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13
Dust the bars with powdered sugar before serving; the bars will keep covered and chilled, for 3 days.
