Preheat oven to 325 degrees and line a baking sheet with a silicon baking mat or parchment paper.
Zest lemons (2 lemons and will need 6 teaspoons of zest) and juice lemon (need 2 tablespoons juice)
In small bowl, using a fork combine 2/3 cup granulated sugar with 3 teaspoons of zest. Set aside.
In a medium bowl, whisk together cake flour (see note), baking powder, and salt. Set aside.
In a bowl of a stand mixer, cream together the butter, powdered sugar and lemon sugar until light and fluffy. Add in the eggs, vanilla, lemon extract paste and blend well. Then add in the lemon juice and mix again.
Slowly add in the dry ingredients and mix until combined. Do not overmix the dough. If the dough is too sticky, place bowl in refrigerator for 20 minutes before forming the cookie dough balls and baking.
I used a one tablespoon cookie scoop to measure out the dough for these lemon cooler cookies. Place on prepared baking sheet and flatten just slightly. Bake for 16 - 19 minutes or until the centers are puffy and the cookies are light golden brown on the bottom. Time will depend on your oven. Remove the cookie sheet to a wire rack and allow to cool for 5 minutes before coating them with powdered sugar.