Combine granulated sugar and lemon zest in a small bowl, rubbing the zest into the sugar until fragrant.
Preheat oven to 350°F (175°C) and prepare baking sheets with parchment paper.
Cream together butter, sugar, and lemon zest in a large bowl until light and fluffy.
Add egg, lemon juice, and vanilla extract, mixing until smooth.
Gradually add flour, baking soda, baking powder, and salt; mix until no dry streaks remain.
Scoop dough into balls, roll in lemon sugar, and place on prepared sheets.
Bake cookies for 9-11 minutes until slightly crackly and set around edges.
Allow cookies to cool for a few minutes before transferring to a cooling rack.