Sift 1 ¼ cups all-purpose flour in a bowl. Add cold, sliced 1 stick unsalted butter, ⅓ cup powdered sugar, 2 pieces egg yolk, 1 teaspoon lemon zest, and ¼ teaspoon vanilla paste.
Use your hands to work the mixture into a smooth dough. Be patient—it will take some time. Stop kneading as soon as the dough feels soft; over-kneading can make the cookies too firm. Wrap the dough in plastic wrap and let it rest in the fridge for at least two hours, or ideally overnight.
Remove the dough from the fridge and divide it in half. Return one half to the refrigerator and leave the other on the counter for about 15 minutes to soften slightly. The dough should remain firm but pliable enough to roll out. Briefly knead it with your hands to ensure it is evenly smooth.
Roll out the dough on a floured work surface to a thickness of ⅛ inch (3 mm), then cut out your shapes. I used a flower-shaped cookie cutter about 2 inches (5 cm) in size. If you are making cookies with a hole in the top layer, be sure to prepare an equal number of tops and bottoms.
Gather the scraps of dough and knead them into a cylinder. Wrap the dough in plastic wrap and refrigerate until it firms up slightly. Once chilled, roll it out and cut out more shapes.
Once you have finished working with the first half of the dough, take the second half out of the fridge and prepare the cookies the same way.
Carefully transfer the cut-out Linzer shapes to a parchment-lined baking sheet using a flat knife or spatula.
Bake the cookies in a preheated oven at
350 °F for 6-8 minutes. Arrange the upper parts with the hole next to each other and dust them with ⅓ cup powdered sugar. Spread a layer of jam on the bottom cookie, then gently place the sugar-dusted top piece on it to create a sandwich.