Adjust oven rack to the middle position and preheat oven to 350F degrees. Line two baking sheet pans with parchment paper. (You only bake them one pan at a time but it's nice to have a cooled pan ready to go right when the first batch comes out).
In a medium bowl, combine the 2 ½ cups flour, 1 tablespoon cornstarch, ½ teaspoon baking soda, and ¼ teaspoon salt.
In the bowl of a food processor fitted with a blade, pulverize the ⅔ cups freeze-dried strawberries into a powder.
In the bowl of a stand mixer fitted with a paddle, beat the 1 cup (or two sticks) butter on medium speed until creamy, about 1 minute. Add the 1 ¼ cups sugar and beat on medium speed until light and fluffy, about 2 minutes. Add the egg, the yolk, and the 2 teaspoons of vanilla, and beat on medium speed until combined. Add the flour mixture and beat on low speed until just combined.
Dump the dough out onto counter or work surface and divide it into three equal portions. Put one-third of the dough into the mixer and add ½ teaspoon of lemon zest. Mix on low speed until the zest it fully incorporated, only 5 to 8 seconds. This will be your vanilla portion. Remove the dough and set aside.
Add another third of the dough to the mixer and add the powdered strawberries and the remaining ½ teaspoon of lemon zest. Mix on low speed until totally combined, about 10 to 15 seconds, then remove the dough. This will be your strawberry portion. Quickly wipe out the bowl of the mixer.
Add the last third of the dough to the mixer. Add the 2 ½ tablespoons of cocoa powder, plus ¼ tsp espresso powder, and mix on low speed until totally combined, again about 10 to 15 seconds.
Pinch small portions (about ½ oz or ½ tablespoon size) of the vanilla dough until all the dough has been portioned. Repeat with the strawberry and then the chocolate dough. You will now have several small balls of all the dough ready to be combined.
You can create your Neapolitan cookies a few different ways. I prefer to take one piece of each dough, lightly squish them side by side together and then insert into the cookie scooper. Press them in firmly but not super tight, then remove with the click of the scooper. Repeat until you've combined them all. This is my favorite way because most people like to be able to bite each flavor individually and this is the prettiest method. 2. If you like to combine the colors to mix and marble a little more, don't worry about lining them side-by-side and instead kind of combine haphazardly. Again place into the cookie scooper. 3. Some bakers make the balls and then randomly place them into a loaf pan, pressing together slightly. Then scoop each cookie out of the combined dough. This method is super easy if you don't care if the flavors remain distinctly separate. 4. You can also just roll the balls into one bigger ball with your hands if you like. Top with a generous amount of sprinkles, if using. I would do this pretty quickly. As the dough sits, it dries out just enough that the sprinkles have a harder time adhering to the cookies. If this happens, kind of press the sprinkles onto the cookie. Place 6 or 7 cookies on the baking sheet, about 2 1/2-inches apart. Bake for 11 to 12 minutes, until the sides are set and the cookies are puffed. Do not let the edges start to change color, they're better just barely golden on the bottom (in my opinion and my taste-testers').
Remove the baking sheet to sit on top of your stove and let the cookies cool for 10 minutes.
Transfer the cookies to a wire rack and let them cool completely. Cookies can be stored in an airtight container at room temperature for up to 2 days.