Combine flour, butter, and 1/2 cup powdered sugar using a pastry blender or 2 forks, until the butter is the size of small peas.
Press into the bottom of a 13 x 9 baking dish. Bake for 20 minutes.
Remove and allow to cool slightly.
While the crust is cooling, combine the eggs, zest, sugar, juice, baking powder, and salt in a large mixing bowl, and beat for about 2 minutes, or until the mixture is a light yellow color.
Pour over the crust and bake for 30 minutes, or until the filling is nearly set. (It should jiggle slightly.)
When cooled, sprinkle powdered sugar over lemon squares.