In a large bowl, whisk together the flour, powdered sugar, salt, and orange zest.
Add the cold butter, and using your fingertips or a pastry blender, cut the butter into the dry ingredients until the mixture resembles coarse crumbs.
Stir in the vanilla sugar, egg, grated apple, and orange juice. Knead until a dough forms. Wrap the dough in plastic wrap and refrigerate for 30 minutes to rest.
Preheat the oven to 350°F (180°C) and line a baking sheet with parchment paper.
On a lightly floured surface, roll out the dough to a 3-4 mm thickness. Use cookie cutters to cut out round shapes. Cut a smaller hole in the center of every other cookie.
Place the cookies onto the prepared baking sheet and bake for 10-12 minutes, or until lightly golden brown.
Let the linzer cookies cool completely. Spread the plain cookies with apple-orange jam or preserves, and top with the cookies that have a hole in the center to create a sandwich.
Before serving, dust with powdered sugar and garnish with apple slices and orange zest, if desired.
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