Combine the flour, baking powder, and salt together in a bowl. Set aside.
With clean fingers, rub the sugar and lemon zest together until fully incorporated. Combine with the butter in the bowl of a stand mixer, and cream together on medium-high until light and fluffy (4-6 minutes), scraping down the sides of the bowl as needed.
Add the egg, mixing until incorporated, then the lemon juice and vanilla.
Comine the wet and dry ingredients, and mix until just combined.
Chill the dough for 30 minutes before rolling into slightly flattened ⅛ cup balls and baking on a parchment-lined cookie sheet for 12-14 minutes. The edges will be set but the tops of the cookies should not brown.
Let the cookies fully cool before whisking the powdered sugar and lemon juice together, and dipping each cookie into the glaze.
Recipe by The Kitchen Paper at http://c02.ddd.mwp.accessdomain.com/iced-lemon-cookies/