Place flour, granulated sugar, ½ tbsp lemon zest, and ½ cup butter into a food processor. Process until well mixed.
Lightly beat yolks and vanilla together. Then slowly pour into the food processor. Process just until dough forms; make sure not to over process.
Transfer dough onto a floured surface. With a rolling pin, roll dough to about ¼" thick (cookies have to be slightly thin because they will be doubled in thickness when sandwiched).
Form shapes with cookie cutter. With spatula, place on baking tray at least 1" apart.
Knead remaining dough together and repeat the rolling process until you have formed enough shapes.
Once ready, bake for around 10 to 15 minutes (depending on size) until firm. Do not brown the sides. Cool on a cooling rack.
In a clean bowl, beat all lemon filling ingredients with an electric mixer until creamy. Use a butter knife to spread filling on a cooled cookie, then sandwich with another. Repeat steps until all cookies are sandwiched.
Use remaining egg white as eggwash. Beat the egg whites, brush onto the cookie tops (only half of them for sandwich tops), and sprinkle with sugar before baking.