Preheat oven to 350 degrees F. Line a 9x9x2-inch baking pan with foil, extending foil over the pan edges; set aside. In a medium bowl, combine flour, oats, apple pie spice, baking soda, and salt; set aside.
In a large bowl, combine butter and shortening. Beat with an electric mixer on medium to high speed for 30 seconds. Add brown sugar. Beat until combined, scraping bowl occasionally. Beat in egg, maple syrup, and vanilla until combined. Beat in as much of the flour mixture as you can with the mixer. Using a wooden spoon, stir in any remaining flour mixture. Stir in nuts and dried apples. Spread dough into the prepared baking pan.
Bake in the preheated oven for 25 minutes or until a toothpick inserted near the center comes out clean. Cool in pan on a wire rack for 30 minutes.
Reduce oven temperature to 325 degrees F. Using the edges of the foil, lift the uncut cookies out of the pan. Place on a cutting board. Carefully remove foil. Using a serrated knife, cut mixture into thirds crosswise. Cut each portion into 3/4x3-inch slices, making a total of thirty 3/4x3-inch slices. Place slices, cut sides down, on ungreased cookie sheets. Bake for 10 minutes. Turn slices over; bake for 10 to 15 minutes more or until dry and crisp. Transfer cookies to wire racks; let cool.