Preheat the oven to 325 degrees F (165 degrees C).
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.
Bake for 25 minutes in the preheated oven, or until firm and lightly browned. 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.
Bake for another 25 minutes in the preheated oven, until set. Dust with remaining confectioners' sugar when cool.