Preheat the oven to 350°F. Cream the butter and powdered sugar. Add in both flours and mix well until slightly tacky.
Press the crust mixture into a 9-inch square baking dish using your fingers to spread into the corners smoothly. Bake the crust until light golden brown, about 20 minutes.
Meanwhile, prepare the filling. Beat the eggs, sugar, lemon juice and zest in a large bowl. Whisk in the flour, baking powder and salt.
Once the crust has finished baking, pour the filling on top of the warm crust.
Return the pan to the oven and bake another 20 minutes until the edges have browned slightly. Cool completely then refrigerate the pan for 1 to 2 hours before cutting.
Remove the lemon squares from the pan and sprinkle generously with powdered sugar from a fine mesh strainer.