Position a rack in the center of the oven and preheat the oven to 325 (F). Line two half sheet pans with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda and salt.
In the bowl of a stand mixer, combine the sugar and fresh zest. Use your fingers to rub the zest into the sugar until clumpy and aromatic—this will help release oils from the zest that will absorb into the sugar. Affix the bowl into the stand mixer fitted with a paddle attachment and add the butter. Beat on medium-high until light, fluffy, and doubled in volume, 2 to 3 minutes. Use a rubber spatula to scrape down the bottom and sides of the bowl. Reduce the mixer to its lowest setting and add the egg, sour cream, and almond extract, scraping the bottom and sides of the bowl as necessary. With the mixer still on low, add the dry ingredients and beat until just combined. Use a 2-tablespoon cookie dough scoop to portion the dough onto the prepared sheet pans, leaving at least 3 inches between each dough ball. Lightly spray the bottom of a glass with cooking spray and dip into the bag of cake flour. Gently press the bottom of the cup on top of each mound of dough and flatten until you get a 1 1/2-inch circle, flouring the bottom of the cup as needed and smoothening out the sides with a wet finger (see baker's notes).
Bake for 16 to 18 minutes, or until the cookies are pale yellow and barely starting to brown on the bottoms. Cool the cookies on the pans on a wire rack for 5 minutes, before transferring to the rack to cool completely before frosting.