Position racks in the center of the oven and preheat the oven to 325°F. Line cookie sheets with parchment paper.
In a large bowl, use an electric mixer to beat together the butter, powdered sugar, and sugar until light and fluffy. Blend in the eggs, vanilla, and lemon extract until smooth. In a medium bowl, whisk together the cake flour, baking powder, and salt. Stir the dry ingredients into the butter mixture. Add the lemon juice and mix until everything is just combined (do not overmix).
If the dough is too sticky to work with, refrigerate for 20 minutes. Using a mini cookie scoop (or a tablespoon), scoop the dough into approximately 1-inch balls. Space the balls at least 1 inch apart on prepared cookie sheets and flatten them slightly. Bake for 15 to 18 minutes or until the centers are puffy and the cookies are light golden brown on the bottom. Remove the cookie sheet to a wire rack and allow to cool for 5 minutes.
While cookies are baking, combine remaining 1 cup powdered sugar and 2 teaspoons lemon zest in a large paper lunch sack or gallon-sized plastic baggie. After 5 minutes of cooling time, remove 4 to 5 warm cookies from the sheet and carefully place in the powdered sugar. Gently shake and roll the bag around until the cookies are coated with powdered sugar. Remove the cookies from the bag, shaking off excess powdered sugar, and allow them to finish cooling on a wire rack. Repeat until all of the cookies are coated with powdered sugar.
If you don’t have cake flour on hand, you can easily make your own. Measure 3 cups of regular flour into a bowl. Use a tablespoon to remove 6 tablespoons of flour from the bowl (put it back into your flour container). Add 6 tablespoons of corn starch to the bowl (to replace the flour you removed). Sift the flour and cornstarch mixture into another bowl by pouring it into a fine mesh strainer and tapping it with the palm of your hand. Repeat this process 4 to 5 more times until mixture is well combined and aerated. Proceed with recipe using your homemade cake flour.
Bottled lemon juice works fine in this recipe, but since you’ll already need several lemons for the zest, it’s tastiest to go ahead and use freshly-squeezed lemon juice.
Lemon extract provides an extra lemony punch, but you may leave it out if you don’t have it.
Finely grated lemon zest works best in this recipe, particularly in the powdered sugar coating. Either use a microplane for zesting, or if your zest is coarse, you can finely chop it with a knife before adding to the recipe.