Make the cookie dough: If using blanched whole almonds, turn half of the almonds into a food processor and process to a coarse meal, about 20 seconds (fig. 1.1). Transfer the ground almonds to a medium bowl. Process the remaining almonds to a very fine meal, 30 to 40 seconds. Add this batch to the first batch and stir well. If using almond flour, turn it in a medium bowl. Measure 4 ounces of the ground almonds or of the almond meal into a small bowl and set aside. Stir the cake flour, cinnamon, lemon zest, and salt into the larger quantity of almonds and rub the mixture with your fingertips until well combined. 

Turn the egg whites and superfine sugar into a clean stand-mixer bowl and set the bowl snugly onto saucepan filled with about 2 inches of water; the water should not touch the bottom of the bowl. Set the saucepan over medium heat and whisk the egg whites and sugar, allowing the water underneath to reach a bare simmer, until the mixture is opaque and frothy (fig. 2.1) and registers 130 degrees on a clean instant-read thermometer. Attach the bowl to the stand mixer fitted with the whisk attachment and beat on medium-high speed until the egg whites are thick and glossy, with slightly drooping tips (fig. 2.2), about 5 minutes. Remove the bowl from the mixer and knock the meringue off the whisk attachment back into the egg white mass. Add the almond meal mixture and fold with a rubber spatula (fig. 2.3) until a fairly firm and only slightly sticky dough forms. Turn the dough onto a sheet of parchment paper and place another sheet of parchment on the top. Press the dough into a rectangle with your hands, and then roll it out into a rectangle measuring about 12 by 8½ inches by ⅜ inch thick (fig. 2.4). Slide the dough, sandwiched between the parchment sheets, onto a baking sheet and refrigerate for at least 3 hours or up to overnight. 

Make the icing: Combine the egg white, lemon juice, and confectioners’ sugar in the bowl of a stand mixer fitted with the whisk attachment. Beat on medium-high speed until the icing is opaque and glossy but fluid enough to flow, about 3 minutes. Pour the icing into a 1- or 2-cup liquid measuring cup, scraping the mixer bowl with a rubber spatula. 

Line 2 baking sheets with silicone baking mats or parchment paper. Fill a small bowl with water. Remove the dough from the refrigerator, lift off the top sheet of parchment, flip the parchment with dough on it, and then lift off the parchment. Pour about two-thirds of the icing onto the center of dough rectangle and use an offset icing spatula to “flood” it smoothly and evenly over the surface, spreading it all the way to the edges (fig. 4.1). Dip a 2-inch star cookie cutter in the bowl of water, shake off the excess, and cut out stars one at a time, pushing the cutter through the icing and dough (fig. 4.2). Lift the cutter; the cookie will remain inside it. Holding the cutter tightly, shake the cookie out onto the palm of your hand (fig. 4.3) with a quick downward thrust of the wrist. If the cookie does not shake free, very carefully use your fingers to push the dough up and out of the top of the cutter. Slip the cookie onto one of the prepared baking sheets and sprinkle with sparkling sugar (fig. 4.4) if desired. Continue to cut out stars, washing and dampening the cutter it after each cookie; space the cookies about ½ inch apart on the baking sheet. When you have nothing but scraps of dough (fig. 4.5), use the spatula to “plane off” as much of the icing as possible from the scraps and return the icing to the measuring cup. Sprinkle a handful of the reserved ground almonds or almond flour onto the scraps, gather them up, and knead (fig. 4.6) until they match the consistency of the original dough, adding more almond flour as necessary. Roll the dough out to a thickness of ⅜ inch, flood with icing, and continue to cut out stars. Repeat a third and final time. You should have about 24 cookies. Let the cookies dry, uncovered, at room temperature overnight.

Adjust the oven racks to the upper-middle and lower-middle positions. Place a baking sheet on the upper rack (it will prevent the cookies from browning) and heat the oven to 300 degrees. Bake the cookies one baking sheet at a time until the bottoms are tawny and tips have begun to color but the icing is still white, 12 to 14 minutes. You can leave the cookies in the oven longer, so long as the icing remains white. Pay close attention! It is important not to overbake or underbake. Let the cookies cool on the baking sheet. Store the cookies in an airtight container between sheets of waxed or parchment paper; they will keep for a couple of weeks.