Preheat oven to 350°F. Grease and line an 8x8 inch pan with parchment paper, leaving an overhang to use as a sling when removing the bars from the pan.
In a large mixing bowl, add sugar and lemon zest and work the lemon zest into the sugar using you fingers. Next, add the butter and cream the butter and sugar mixture together until light and fluffy.
Add vanilla, egg, salt, and baking powder and mix until combined.
Pour in the flour and mix until you have a thick dough.
Add the dough to the parchment lined pan and press it evenly across the pan using your fingertips. *You may want to chill the dough in the pan for about 20 minutes to make it easier to spread.
Bake the lemon cookie bars for 20 minutes until they are just golden brown around the edges.
Place the pan on a wire rack to cook completely before removing the bars from the pan using the sling method.