In a large mixing bowl, whisk together flour, baking powder, and sea salt.
In another bowl, combine butter, eggs, sugar, lemon juice, vanilla extract, and lemon zest. Whisk until smooth.
Add wet ingredients to dry ingredients, stir together until a soft dough forms - it should look runny like cake batter.
Chill the dough for at least 2 hours to overnight. The dough will firm up more but will still be a bit sticky.
Preheat oven to 350 degrees, and line a large baking sheet with parchment paper.
Prepare two shallow bowls, one with granulated sugar and the other with powdered sugar.
Shape the dough into balls using a 2 tbsp scoop. You can dust the scoop with some powdered sugar beforehand to keep the dough from sticking.
Roll each dough in granulated sugar, then in powdered sugar until fully coated.
Place on the baking sheet 2 inches apart, working in batches if they don't all fit (keep any dough that's not being baked right away in the fridge).
Baking for 9-12 minutes until they spread a little and get puffy with a cracks on top.
Cool for 10 minutes, then use a spatula to carefully transfer to a cooling rack to cool completely. They'll be soft and delicate but will set as they cool. Enjoy!