In a large bowl, whisk together the flour, powdered sugar, baking powder, and salt.
Add the cold, cubed butter and cut it into the dry ingredients until the mixture resembles coarse crumbs.
Add the egg and grated apple, then knead until a dough forms. Wrap in plastic wrap and chill in the refrigerator for 30 minutes.
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). Cut out circles using a cookie cutter. Cut a smaller hole in the center of every other circle.
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 vanilla pastry cream and top with the cookies with the holes.
Before serving, dust with powdered sugar and garnish with thin apple slices.
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