Preheat oven to 350°F (175°C) and line two cookie sheets with parchment paper.
In a bowl, whisk together flour, baking powder, baking soda, and salt, then set aside.
Cream together butter and sugar until fluffy, then mix in egg, vanilla, and lemon zest.
Gradually add dry ingredients to wet ingredients, mixing until dough forms.
Roll dough into balls, coat in lemon sugar, and flatten slightly on prepared cookie sheets.
Bake for 9-10 minutes, then cool on a wire rack.