Preheat the oven to 350 degrees F.
In a large bowl, combine the flour and sugar.
Cut the softened butter stick into four pieces and add it to the bowl of sugar and flour. Using a pastry cutter, cut the butter into the mixture until it clings together and is crumbly.
Pour the shortbread crust into a 9X13 inch glass baking pan and press in until the bottom is covered evenly.
Bake the crust for 20 to 25 minutes, until just turning golden. Remove from the oven to set aside and cool.
While the crust is baking, make the filling. In a large mixing bowl, use an electric hand mixer to whisk together the eggs, white sugar, and lemon juice.
In a separate bowl, combine the flour, baking powder and lemon zest. Add these dry ingredients to the egg mixture and mix together. The batter will be very runny.
Pour the lemon batter evenly over the baked, cooled crust.
Bake for approximately 25 minutes. It should be a light golden brown.
Remove it from the oven and allow it to cool before cutting and serving.
Dust the top of the bars with powdered sugar (try using a fine sieve or sifter) and cut into squares.