In a large bowl, whisk together the flour, powdered sugar, salt, and lemon zest.
Add the cold butter and cut it into the dry ingredients using a pastry blender or your fingertips until the mixture resembles coarse crumbs.
Stir in the vanilla sugar, egg, mashed banana, and lemon juice. Knead until a smooth dough forms. Wrap in plastic wrap and refrigerate for 30 minutes to rest.
Preheat oven to 350°F (180°C) and line a baking sheet with parchment paper.
Roll out the dough to a thickness of about 1/8 inch (3-4 mm). Use a round cookie cutter to cut out cookies. Cut a smaller hole in the center of half of the circles.
Place the cookie rounds on 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 lemon-banana jam or curd and top with the cookies with the holes.
Before serving, dust with powdered sugar and garnish with lemon slices and banana slices.
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