Preheat oven to 375 degrees F and prepare a 9x9 square cake pan coated with butter or pan spray and lined with parchment paper
In a medium bowl combine the flour, baking powder and salt; set aside
In the bowl of the electric mixer, cream together the butter, granulated sugar and lemon zest until smooth and creamy; Scrape down the sides in between mixing
Add the eggs, lemon juice and vanilla extract and continue mixing until all ingredients are combined (it will look clumpy)
On low speed, add the dry ingredients to the mixing bowl and mix until fully combined (scrape down the sides in between mixing)
Evenly spread the sugar cookie batter into the prepared cake pan
Bake for 13-14 minutes or until the center is set (do not overbake, the bars should be light in color)
Remove the bars from the oven and allow them to cool completely before adding the frosting
Prepare the frosting while the bars cool