I adapted an old oatmeal raisin cookie recipe I had to match a more autumnal feel, and it turned out really good. The apples came through nicely and the cookie itself is light, soft, and nicely crumbly.
Beat white sugar, brown sugar, eggs, butter, shortening, baking soda, cinnamon, vanilla extract, salt, baking powder, and nutmeg together in a bowl with an electric mixer on medium speed until smooth; stir in oats, apples, and flour until dough is evenly combined. Drop dough by rounded tablespoons, about 2 inches apart, onto baking sheets.
Bake in the preheated oven until cookies are lightly browned, 9 to 11 minutes. Transfer cookies to a wire rack to cool, 3 to 5 minutes.