In a medium bowl, stir together the flour, cornstarch and 1.5 cups icing sugar.
In the bowl of a stand up mixer fitted with the paddle attachment, beat the granulated sugar, 2 cups butter and salt until light and fluffy, about 2 minutes. Add the egg yolks and 4 tsp vanilla extract and beat until combined, about 15 seconds. Gradually add in the flour and cornstarch mixture at low speed, scraping down the sides of the bowl, until mixture starts to clump together, about 20 seconds.
Divide the dough into 4 sections, roll each into a log about 2 inches thick, wrap each log in plastic and refrigerate for a minimum of 2 hours and up to 2 days.
Preheat the oven to 325ºF.
Unwrap one of the dough logs and slice into rounds of about 1/4 inch thick. Place the rounds, 1 inch apart, on a cookie sheet lined with parchment paper. Bake in the preheated oven for 8-10 minutes (check at the 8 minute mark to make sure they don’t brown at the bottom).
Remove from the oven and cool on the baking sheet for 2 minutes. Transfer the cookies to a cookie wire rack to cool down completely, about 30 minutes. Repeat the process with the remaining 3 logs of dough. You will get about 72 cookies.
Make the espresso filling:
Melt butter into hot or warm espresso. Using a mixer, or by hand, add the espresso mixture into the sugar in increments until the mixture is creamy, thick and thoroughly combined.
Make the lemon filling:
Stir together the lemon juice and 1 Tb water in a small bowl. Beat the remaining 2 Tbs butter on medium speed until creamy, about 1 minute. Beat in 1/4 tsp salt and 1/2 tsp vanilla. Add the icing sugar in increments, alternating with the lemon mixture, beating on low speed until incorporated after each addition. Beat in remaining 1 Tbs water, 1 tsp at a time, until consistency is thick but spreadable. Finally, stir in the lemon zest.
Transfer lemon filling and espresso filling to piping bags. Turn 36 cookies upside down and pipe the lemon or the espresso filling, about 1 Tbs, on each of them. Cover with the remaining 36 cookies.