Preheat oven to 375 degrees F. Line a 9x13 pan (or quarter bakers sheet) with parchment paper. Set aside.
Mix butter with an electric mixer on high for 1 minute, until lighter in color. Add in sugar, egg, vanilla extract and lemon zest, and mix again.
Combine dry ingredients and whisk lightly, so that the salt and baking powder are well incorporated into the flour. Pour into the butter mixture and mix well.
Transfer dough to prepared pan and press down so that dough is spread evenly across entire pan. Bake for 20 minutes. Cool 20 minutes.
Whisk lemon glaze ingredients and pour onto warm cookie bars. Spread glaze across cookie bars with a rubber scraper. Let fully cool to set. Cut into 30 squares. Store leftovers in an airtight container.