Preheat your oven to 350°F (180°C) and line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, powdered sugar, and baking powder.
Add the cold butter, and using your fingertips or a pastry blender, cut it into the dry ingredients until the mixture resembles coarse crumbs.
Grate in the lemon zest, then add the lemon juice and egg. Mix until a smooth dough forms.
Gently fold in the grated apple. Roll the dough out to about 5 mm (approximately 1/4 inch) thickness.
Use round cookie cutters to cut out shapes. Cut out the center of every other cookie with a smaller cutter to create the classic Linzer shape.
Bake for 12-15 minutes, or until the cookies are lightly golden brown. Be careful not to let them burn.
Let the cookies cool completely. Spread apricot jam on the flat (uncut) cookies, then top with the Linzer rings to create a sandwich.
Before serving, dust the Linzer cookies with powdered sugar for an extra touch of elegance.
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