In a stand mixer or mixing bowl, beat butter for 30 seconds on medium high speed. Add sugars, baking powder, baking soda, salt, and apple pie spice. Beat until combined, scraping sides of bowl once.
Add eggs and vanilla and beat again to combine. Add flour, oatmeal, and apples. Beat again to mix well.
Use a large cookie scoop to measure out 10 scoops of dough about 4 inches apart onto two cookie sheets. Bake for 10-13 minutes or until edges are light brown.
Cool for 1 minute on the cookie sheets before moving to wire cooling racks. Cool completely before icing.
Combine apple cider and powdered sugar until there are no lumps. Add a little apple cider as needed to reach a consistency that the icing can be drizzled over the cookies.
Notes
Adapted from Better Homes and Gardens CookbookI think the cookies taste better the next day.