Hard boil 3 of the eggs, then remove the yolk. Using a spoon, press the egg yolks through a fine-mesh sieve, until it turns into a paste.
Using a fork, mix together with the raw egg yolks to create a paste.
Mix together butter, sugar, lemon zest, and your egg yolk paste until incorporated.
Add in the flour and milk and knead until you have a cohesive, smooth dough.
Cover the dough and transfer to the fridge to chill for 60 minutes.
Preheat oven to 390° Fahrenheit (200° Celsius).
On a surface dusted in flour, roll out the dough to ⅒ inch (3 mm) thickness, and cut out your favorite shapes, cutting out the middle for half of them.
Transfer cookies to baking sheets covered in parchment paper or fitted with baking mats and bake for 8 to 10 minutes on the middle rack until just starting to turn golden around the edges.
After baking, carefully pull the baking sheet or parchment paper onto a cooling rack.
Dust top cookie with powdered sugar.
Using spoons, put about ½ teaspoon of jam on each bottom cookie, then assemble the cookies by placing the sugar-dusted top cookie on the jam-covered bottom cookie.
