Position a rack in the center of the oven and preheat to 350ºF. Grease a 9 by 13 by 2-inch baking sheet and set aside for later use.

In a food processor, combine the butter, sugar, egg, heavy cream, lemon juice, sea salt, and flour and pulse until the dough starts to gather together in big clumps. Dump out onto a clean surface and gather it together. Flatten the dough with floured hands and press it into the greased baking sheet that was prepared earlier. Build a 1/2-inch wall on each side. Chill in the refrigerator for at least 15 minutes prior to baking. Bake the crust for 20 minutes or until very lightly browned. Let cool on a wire rack. Leave the oven on.

In an electric mixer fitted with the paddle attachment, cream the butter and the sugar together until the butter turns a light yellow. Add the egg, heavy cream, and lemon juice and continue to mix. When everything is well incorporated, add the salt. Lastly, add the flour in two batches until the just mixed. Dump out onto a clean surface and gather it together. Flatten the dough with floured hands and press it into the greased baking sheet that was prepared earlier. Build a 1/2-inch wall on each side. Chill in the refrigerator for at least 15 minutes prior to baking. Bake the crust for 20 minutes or until very lightly browned. Let cool on a wire rack for at least 10 minutes. Leave the oven on.

In a medium bowl, combine the sugar and lemon zest. Using your finger tips or the back of a wooden spoon, mash the lemon zest into the sugar. This will help disperse the lemon oils through the sugar.

In a large bowl, whisk together the eggs, sugar and lemon zest mixture, lemon juice, and flour.

Pour the mixture over the crust and bake for 30 minutes or until the 'jiggliness' is gone from the lemon layer. Let cool to room temperature before cutting into squares and dust with confectioners' sugar.