Preheat oven to 350F.
Beat butter and both sugars in bowl of stand mixer on speed 2 for 3 minutes.
Add eggs one at a time, scraping down sides and beating until fully combined.
Stir in vanilla extract.
Slowly add flour, baking powder, salt, and cinnamon, mixing until combined.
Stir dried apple into dough.
Divide dough in half.
Shape each half into 10″ x 4″ rectangle, using floured hands.
Set loaves 3″ apart on a parchment paper-lined baking sheet.
Bake for 30 minutes or until the dough is set.
Leaving the oven on, remove the baking sheet from the oven, and cool biscotti loaves for 15 minutes on cookie sheet.
Using a chef’s knife, cut the loaves into diagonal slices, 3/4″ thick.
Place slices on cookie sheet with the cut sides down. Bake for 10 minutes.
Turn slices over, and bake for 10 minutes more.
Remove biscotti from oven, and allow to cool completely on a cooling rack.
Combine powdered sugar, cinnamon, and cider, stirring until smooth.
Using a spoon, drizzle glaze over biscotti.
Glaze should set in 5-10 minutes.