Cream the softened butter and sugar until smooth and lightly fluffy.
Add the egg white, salt, and vanilla sugar (or vanilla + sugar), mixing until incorporated.
Add the flour in two additions, mixing just until the dough forms a soft, cohesive ball.
Flatten into a disk, wrap, and refrigerate for at least 30 minutes.
Preheat oven to 325°F (160°C) and line baking sheets with parchment.
Roll the chilled dough to 4–5 mm thickness on a lightly floured surface or between parchment sheets.
Cut an even number of shapes. Using a smaller cutter, create a window in half the cookies.
Arrange cookies with space between them and bake for 10–12 minutes, until the edges are barely golden. Cool completely.
Spread a thin layer of jam on each solid cookie. Dust the cut-out cookies generously with powdered sugar. Place a dusted cookie on each jam-coated base. Let set 10–15 minutes before serving.