In a food processor, or the bowl of a stand mixer, mix together the sugar and lemon zest until well combined and the sugar is lightly yellow and fragrant.
Add the softened butter to the sugar and mix until light and fluffy.
Add the vanilla, egg, and lemon juice and mix well, scraping down the sides of the bowl as needed.
Add the salt, baking powder, baking soda and flour and mix until combined.
Chill the dough for one hour.
Preheat the oven to 350°F. Line 2 cookie sheets with parchment paper or silicone baking mats. Set aside.
Roll the cookie dough into tablespoon sized balls, roll them in powdered sugar and place them 2 inches apart on the baking sheet.
Bake for 10-11 minutes or until they are just starting to brown on the edges and are no longer shiny. Do not over bake the cookies.
Allow the cookies to cool on the baking sheet for 5-10 minutes before moving to a wire rack to cool completely. Store in an airtight container at room temperature for 5-7 days, or freeze for up to 3 months.