Preheat the oven to 350 degrees. Grease a 9x13 inch pan.

For the crust, cream the butter and just 1/2 cup sugar together until the color lightens (a few minutes). Mix just 2 cups of the flour and the salt on low until just combined with the butter. With floured hands, press the dough into the pan, making a 1/2 inch edge on the sides. Chill for 15 minutes. Bake for 15-20 minutes, until lightly browned. Let cool on a wire rack. Leave the oven on.

For the filling, whisk together the eggs, the remaining 3 cups sugar, lemon zest, lemon juice, and the remaining 1 cup flour. Pour the filling over the crust (crust doesn't need to be cooled completely). Bake 30-35 minutes, until filling is set.

Let cool to room temperature before cutting into squares. Dust with powdered sugar.