Prepare the ingredients. Have the butter softened to about 68°F (20°C), pliable but not shiny or melted. Finely grind the walnuts in short pulses without making a paste. Wash and dry the lemon, then measure the yellow zest and juice. Combine the flour, ground walnuts, and salt in a separate bowl.
Cream the butter and sugars. Beat the butter with the dough portion of granulated sugar and vanilla sugar for about 3 minutes on medium speed, scraping the bowl as needed, until creamy and evenly combined.
Add the eggs and lemon. Beat in the whole eggs, then the additional yolks, until incorporated. Briefly mix in the measured lemon juice and zest.
Mix the dough. Add the dry mixture in several additions on low speed. Stop as soon as the dough holds together, finishing with a spatula if needed. Do not knead for several minutes or taste the raw dough.
Chill the dough. Shape into a flat disk about 1 inch (2–3 cm) thick, wrap, and refrigerate for about 60 minutes. Divide a larger batch into several disks so they chill evenly.
Roll and cut. Heat the oven to 340°F (170°C), conventional, and line baking pans with parchment. Work with half of a base batch or one manageable portion at a time, keeping the rest chilled. Roll between parchment sheets to an even 3/16 inch (5 mm), and cut circles about 1.6 inches (4 cm) across. Gather scraps gently and reroll once. Cut an even number of circles so every finished cookie has two halves. Keep about 1/2 inch (1.25 cm) between circles and use additional trays rather than crowding.
Bake gently. Bake one tray at a time on the middle rack for about 10–12 minutes, until the tops remain pale and the undersides are only very lightly golden. Rotate if the oven browns unevenly. Repeat with the remaining trays; the displayed baking time is for the base batch and increases with more batches.
Cool completely. Let the baked halves firm on the tray for about 5 minutes, then move carefully to a wire rack. Allow at least 20 more minutes and longer if needed until completely cool. Earlier trays can cool while later trays bake.
Fill the cookies. Pair fully cooled halves of similar size. Stir the smooth preserves, then spread a thin layer on the flat underside of a supported cookie half. Set its partner on top, flat side toward the filling, and join with very gentle pressure. Distribute the measured filling across the selected yield.
Coat with sugar. Mix the powdered sugar and the separate coating portion of vanilla sugar in a shallow bowl. Gently cover the top, bottom, and sides of each assembled cookie. Lift carefully and shake off loose excess without squeezing the sandwich.
Allow the flavor to develop. Arrange in a clean airtight container, using parchment between layers. Refrigerate promptly at 40°F (4°C) or below for about 12 hours before serving so the filling and cookie texture can settle together. Follow the preserves label and the storage notes; do not leave the filled cookies on the counter overnight.