Preheat the oven to 350 degrees F.
In a large bowl with electric mixer, beat together the butter and brown sugar.
Add the egg and vanilla extract and beat until well combined.
In a separate bowl, whisk together the flour, oats, cinnamon, nutmeg, baking soda, and salt.
Add the dry ingredients to the butter/sugar and mix until well combined.
Finally, add the shredded apples and mix to combine.
Scoop dough into 2 tablespoon cookie balls and place on parchment paper lined baking sheet, about 2 inches apart, and flatten slightly.
Bake in the preheated oven for 10-12 minutes, until slightly golden and set.
Cool for about 5 minutes on the baking sheet and then transfer to a cooling rack to cool completely.